Found 271 Documents (Results 1–100)
Parametrization of algebraic points of low degree on the hyperelliptic curves \(y^2=x(x^2-n^2)(x^2-4n^2)\). (English) Zbl 07918831
Seck, Diaraf (ed.) et al., Nonlinear analysis, geometry and applications. Proceedings of the third NLAGA-BIRS symposium, AIMS-Mbour, Senegal, August 21–27, 2023. Cham: Birkhäuser. Trends Math., 341-351 (2024).
A numerical representation of hyperelliptic KdV solutions. (English) Zbl 07899964
Reviewer: Ahmed Lesfari (El Jadida)
A family of integrable maps associated with the Volterra lattice. (English) Zbl 07896367
Reviewer: William J. Satzer Jr. (St. Paul)
The cyclicity of a class of quadratic reversible systems with hyperelliptic curves. (English) Zbl 07863177
Reviewer: Joan C. Artés (Barcelona)
The Mumford dynamical system and hyperelliptic Kleinian functions. (English. Russian original) Zbl 1540.35336
Funct. Anal. Appl. 57, No. 4, 288-302 (2023); translation from Funkts. Anal. Prilozh. 57, No. 4, 27-45 (2023).
Reviewer: Piotr Biler (Wrocław)
Computing minimal Weierstrass equations of hyperelliptic curves. (English) Zbl 1541.11057
Reviewer: José María Tornero (Sevilla)
Imaginary quadratic integral points on a hyperelliptic curve of certain type. (English) Zbl 1534.11040
Reviewer: Dimitros Poulakis (Thessaloniki)
Algebro-geometric constructions of a hierarchy of integrable semi-discrete equations. (English) Zbl 1509.37096
Parametric Korteweg-de Vries hierarchy and hyperelliptic sigma functions. (English. Russian original) Zbl 1512.35514
Funct. Anal. Appl. 56, No. 3, 169-187 (2022); translation from Funkts. Anal. Prilozh. 56, No. 3, 16-38 (2022).
New classes of particular solutions to one problem on gyrostat motion. (Russian. English summary) Zbl 1509.70003
Diophantine equations for polynomials with restricted coefficients. I: Power values. (English) Zbl 1500.11028
Reviewer: Dimitros Poulakis (Thessaloniki)
The monotonicity of the ratio of two hyperelliptic abelian integrals for a class of symmetric potential systems of degree eight. (English) Zbl 1498.37095
Reviewer: Valery A. Gaiko (Minsk)
Transcendental number theory. With a new foreword by David Masser. Reprint of the 1990 paperback edition. (English) Zbl 1496.11001
Cambridge Mathematical Library. Cambridge: Cambridge University Press (ISBN 978-1-00-922994-4/pbk; 978-1-00-922993-7/ebook). xiv, 169 p. (2022).
Continued fractions and Hankel determinants from hyperelliptic curves. (English) Zbl 1485.39030
Reviewer: Ahmed Lesfari (El Jadida)
Solving polynomials with ordinary differential equations. (English) Zbl 1487.26020
Reviewer: Olga M. Katkova (Boston)
The classification of traveling wave solutions to space-time fractional resonance nonlinear Schrödinger type equation with a special kind of fractional derivative. (English) Zbl 1477.35060
Invariant algebraic curves and hyperelliptic limit cycles of Liénard systems. (English) Zbl 1478.34041
Reviewer: Weinian Zhang (Chengdu)
Hyperelliptic curves and newform coefficients. (English) Zbl 1487.11064
Reviewer: Francesc Bars Cortina (Bellaterra)
Zero bifurcation diagrams for abelian integrals: a study on higher-order hyperelliptic Hamiltonian systems with three perturbation parameters. (English) Zbl 1473.34024
The number of partitions of a set and superelliptic Diophantine equations. (English) Zbl 1470.11177
Raigorodskii, Andrei M. (ed.) et al., Discrete mathematics and applications. Cham: Springer. Springer Optim. Appl. 165, 35-55 (2020).
Orbits of test particles in three-dimensional Maxwell-Dilaton spacetime: exact analytical solution to the geodesic equation. (English) Zbl 1443.83010
Maximal amplitudes of hyperelliptic solutions of the derivative nonlinear Schrödinger equation. (English) Zbl 1442.35431
MSC:
35Q55
On the number of hyperelliptic limit cycles of Liénard systems. (English) Zbl 1453.34045
Reviewer: Alexander Grin (Grodno)
On the monotonicity of the ratio of some hyperelliptic integrals of order 7. (English) Zbl 1434.34032
Reviewer: Maite Grau (Lleida)
Difference Krichever-Novikov operators of rank 2. (English. Russian original) Zbl 1431.39009
Proc. Steklov Inst. Math. 305, 195-208 (2019); translation from Tr. Mat. Inst. Steklova 305, 211-224 (2019).
Reviewer: Nikolay Dimitrov (Ruse)
Autonomous limit of the 4-dimensional Painlevé-type equations and degeneration of curves of genus two. (Limite autonome des équations 4-dimensionnelles de type Painlevé et la dégénérescence des courbes de genre deux.) (English. French summary) Zbl 1416.34078
Sharp upper bound for amplitudes of hyperelliptic solutions of the focusing nonlinear Schrödinger equation. (English) Zbl 1420.35387
Reviewer: Alessandro Selvitella (Fort Wayne)
Computing integral points on genus 2 curves estimating hyperelliptic logarithms. (English) Zbl 1443.11121
Reviewer: Francesc Bars Cortina (Bellaterra)
A unique pair of triangles. (English) Zbl 1400.14069
J. Number Theory 194, 297-302 (2019); corrigendum ibid. 242, 44-45 (2023).
Reviewer: Juan Tena Ayuso (Valladolid)
Monotonicity of the ratio of two abelian integrals for a class of symmetric hyperelliptic Hamiltonian systems. (English) Zbl 1464.37060
Reviewer: Maite Grau (Lleida)
Improved rank bounds from \(2\)-descent on hyperelliptic Jacobians. (English) Zbl 1406.11057
Reviewer: Francesc Bars Cortina (Bellaterra)
An algebraic construction of a solution to the mean field equations on hyperelliptic curves and its adiabatic limit. (English) Zbl 1400.14087
Reviewer: Ahmed Lesfari (El Jadida)
Zeros of hyperelliptic integrals of the first kind for special hyperelliptic Hamiltonians of degree 7. (English) Zbl 1375.34048
Computing integral points on hyperelliptic curves using quadratic Chabauty. (English) Zbl 1376.11053
Reviewer: Dimitros Poulakis (Thessaloniki)
Families of orthogonal Laurent polynomials, hyperelliptic Lie algebras and elliptic integrals. (English) Zbl 1378.33008
Analytical solutions for geodesic equation in black hole spacetimes. (English) Zbl 1334.83026
Nicolini, Piero (ed.) et al., 1st Karl Schwarzschild meeting on gravitational physics, KSM 2013, Frankfurt am Main, Germany, July 22–26, 2013. Cham: Springer (ISBN 978-3-319-20045-3/hbk; 978-3-319-20046-0/ebook). Springer Proceedings in Physics 170, 43-51 (2016).
Action-angle variables for the Lie-Poisson Hamiltonian systems associated with Boussinesq equation. (English) Zbl 1489.35237
The Chebyshev’s property of certain hyperelliptic integrals of the first kind. (English) Zbl 1353.34041
Mean field equations, hyperelliptic curves and modular forms. (English) Zbl 1377.35100
Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. III: Invited lectures. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-806-3/hbk; 978-89-6105-803-2/set). 331-343 (2014).
Algebro-geometric solutions for the two-component Camassa-Holm Dym hierarchy. (English) Zbl 1349.37066
On commuting differential operators of rank 2. (English. Russian original) Zbl 1308.13036
Sib. Math. J. 55, No. 4, 606-610 (2014); translation from Sib. Mat. Zh. 55, No. 4, 744-749 (2014).
MSC:
13N10
Effective results for Diophantine equations over finitely generated domains. (English) Zbl 1312.11019
Reviewer: Volker Ziegler (Salzburg)
Algebro-geometric solutions and their reductions for the Fokas-Lenells hierarchy. (English) Zbl 1420.37097
Hyperelliptic function solutions with finite genus \(\mathcal{G}\) of coupled nonlinear differential equations. (English) Zbl 1420.35296
Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2. (English. Russian original) Zbl 1306.53013
Trans. Mosc. Math. Soc. 2013, 281-292 (2013); translation from Tr. Mosk. Mat. O.-va 74, No. 2, 339-352 (2013).
Reviewer: Vladimir P. Kostov (Nice)
Effective results for hyper- and superelliptic equations over number fields. (English) Zbl 1274.11085
The monotonicity of the ratio of two abelian integrals. (English) Zbl 1283.34026
Reviewer: Iliya Iliev (Sofia)
The number of zeros of abelian integrals for a perturbation of hyperelliptic Hamiltonian system with degenerated polycycle. (English) Zbl 1270.34057
Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function. (Intégration du réseau de Toda quasi-périodique et périodique par la fonction sigma hyperelliptique.) (English. French summary) Zbl 1279.14044
Reviewer: Ahmed Lesfari (El Jadida)
Pointless hyperelliptic curves. (English) Zbl 1272.11083
Reviewer: Andreas Stein (Oldenburg)
The exact bounds on the number of zeros of complete hyperelliptic integrals of the first kind. (English) Zbl 1270.34058
Reviewer: Iliya Iliev (Sofia)
Siegel’s theorem and the Shafarevich conjecture. (English. French summary) Zbl 1271.11065
On the average number of rational points of bounded height on hyperelliptic curves. (English) Zbl 1239.14017
Reviewer: Roberto Dvornicich (Pisa)
Boutroux curves with external field: equilibrium measures without a variational problem. (English) Zbl 1259.33021
Reviewer: Andrei A. Kapaev (Trieste)
Nonlinear evolution equations and hyperelliptic covers of elliptic curves. (English) Zbl 1254.14041
Reviewer: Ahmed Lesfari (El Jadida)
Memory efficient hyperelliptic curve point counting. (English) Zbl 1222.11079
Reviewer: Andrew Obus (Bonn)
Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in general relativity. (English) Zbl 1213.83039
On \((a, b)\)-balancing numbers. (English) Zbl 1240.11053
Reviewer: Lajos Hajdu (Debrecen)
Systems of uniformization equations along Saito free divisors and related topics. (English) Zbl 1244.35093
Fukui, Toshizumi (ed.) et al., The Japanese-Australian workshop on real and complex singularities, JARCS III, The University of Sydney, Sydney, Australia, September 15–18, 2009. Canberra: Australian National University, Centre for Mathematics and its Applications (ISBN 0-7315-5207-5). Proceedings of the Centre for Mathematics and its Applications, Australian National University 43, 83-126 (2010).
Reviewer: Aleksandr G. Aleksandrov (Moskva)
KdV-Volterra chain. (English) Zbl 1198.35238
Two-cover descent on hyperelliptic curves. (English) Zbl 1208.11078
Reviewer: Takao Yamazaki (Tohoku)
A rigorous study of possible configurations of limit cycles bifurcating from a hyper-elliptic Hamiltonian of degree five. (English) Zbl 1175.37055
Reviewer: Iliya Iliev (Sofia)
Determinant form of the complex phase function of the steepest descent analysis of Riemann-Hilbert problems and its application to the focusing nonlinear Schrödinger equation. (English) Zbl 1175.30039
Reviewer: Sergei V. Rogosin (Minsk)
A direct method to find solutions of some type of coupled Korteweg-de Vries equations using hyperelliptic functions of genus two. (English) Zbl 1220.35147
Solutions of some coupled Korteweg-de-Vries equations in terms of hyperelliptic functions of genus two. (English) Zbl 1187.35203
Manganaro, Natale (ed.) et al., Proceedings WASCOM 2007. 14th Conference on waves and stability in continuous media, Baia Samuele, Sicily, Italy, 30 June – 6 July 2007. Hackensack, NJ: World Scientific (ISBN 978-981-277-234-3/hbk). 72-77 (2008).
Geodesic equation and theta-divisor. (English) Zbl 1183.83018
Macías, Alfredo (ed.) et al., Recent developments in gravitation and cosmology. 3rd Mexican meeting on mathematical and experimental physics, México City, México, 10–14 September 2007. Proceedings. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0496-0/hbk). AIP Conference Proceedings 977, 116-133 (2008).
Nonlinear differential equations of second Painlevé type with the quasi-Painlevé property. (English) Zbl 1166.34057
Reviewer: Galina Filipuk (Warszawa)
On the Heun equation. (English) Zbl 1153.34356
On a necessary condition for one class of hyperelliptic equations to have positive integer solutions. (Chinese. English summary) Zbl 1150.11412
From exact-WKB toward singular quantum perturbation theory. II. (English) Zbl 1139.81348
Aoki, Takashi (ed.) et al., Algebraic analysis of differential equations. From microlocal analysis to exponential asymptotics. Festschrift in honor of Takahiro Kawai. Containing papers presented at the conference on algebraic analysis of differential equations–from microlocal analysis to exponential asymptotics, Kyoto, Japan, July 7–14, 2005. Tokyo: Springer (ISBN 978-4-431-73239-6/hbk). 321-334 (2007).
Reality conditions of loop solitons genus \(g\): hyperelliptic am functions. (English) Zbl 1134.37034
A class of differential equations of PI-type with the quasi-Painlevé property. (English) Zbl 1150.34031
Reviewer: Yuefei Wang (Beijing)
Rational points on certain hyperelliptic curves over finite fields. (English) Zbl 1131.11039
Reviewer: Christophe Ritzenthaler (Marseille)
On cyclotomic hyperelliptic curves and the equation \(x^p-y^p=cz^2\). (Sur les courbes hyperelliptiques cyclotomiques et les équations \(x^p-y^p=cz^2\).) (French. English summary) Zbl 1116.11018
Reviewer: Alain Kraus (Paris)
Some ternary Diophantine equations of signature \((n,n,2)\). (English) Zbl 1159.11012
Bosma, Wieb (ed.) et al., Discovering mathematics with Magma. Reducing the abstract to the concrete. Berlin: Springer (ISBN 3-540-37632-1/hbk). Algorithms and Computation in Mathematics 19, 63-91 (2006).
Reviewer: D. Poulakis (Thessaloniki)
Painlevé property of the Hénon-Heiles Hamiltonians. (English) Zbl 1144.34061
Delabaere, Éric (ed.) et al., Théories asymptotiques et équations de Painlevé. Paris: Société Mathématique de France (ISBN 978-2-85629-229-7/pbk). Séminaires et Congrès 14, 65-82 (2006).
Reviewer: Galina Filipuk (Loughborough)
Hyperelliptic theta-functions and spectral methods: KdV and KP solutions. (English) Zbl 1127.14032
Reviewer: Iskander A. Taimanov (Novosibirsk)
Closed geodesics and billiards on quadrics related to elliptic KdV solutions. (English) Zbl 1122.37041
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