[1] |
Li, J., Singular Traveling Wave Equations: Bifurcation and Exact Solutions (2013), Science Press: Science Press Beijing |
[2] |
Ogawa, T., Traveling wave solutions to a perturbed Korteweg-de Vries equation, Hiroshima Math. J., 24, 401-422 (1994) · Zbl 0812.76015 |
[3] |
Chen, A.; Guo, L.; Deng, X., Existence of solitary waves and periodic waves for a perturbed generalized BBM equation, J. Differ. Equ., 261, 5324-5349 (2016) · Zbl 1358.34051 |
[4] |
Chen, A.; Guo, L.; Huang, W., Existence of kink waves and periodic waves for a perturbed defocusing mKdV equation, Qual. Theory Dyn. Syst., 17, 3, 495-517 (2018) · Zbl 1405.35183 |
[5] |
Zhu, K.; Wu, Y.; Shen, J., New solitary wave solutions in a perturbed generalized BBM equation, Nonlinear Dynam., 97, 2413-2423 (2019) · Zbl 1430.37088 |
[6] |
Zhao, Z., Solitary waves of the generalized KdV equation with distributed delays, J. Math. Anal. Appl., 344, 32-41 (2008) · Zbl 1143.35364 |
[7] |
Hattam, L., Traveling waves solutions of the perturbed mKdV equation that represent traffic congestion, Wave Motion., 79, 57-72 (2018) · Zbl 1465.35352 |
[8] |
Yan, W.; Liu, Z.; Liang, Y., Existence of solitary waves and periodic waves to a perturbed generalized KdV equation, Math. Model. Anal., 19, 537-555 (2014) · Zbl 1488.34329 |
[9] |
Zhang, L.; Han, M.; Zhang, M.; Khalique, C. M., A new type of solitary wave solution of the mKdV equation under singular perturbations, Int. J. Bifurcation Chaos, 30, Article 2050162 pp. (2020) · Zbl 1451.35178 |
[10] |
Fan, X.; Tian, L., The existence of solitary waves of singularly perturbed mKdV-KS equation, Chaos Solit. Fract., 26, 1111-1118 (2005) · Zbl 1072.35575 |
[11] |
Wang, J.; Yuen, M.; Zhang, L., Persisitence of solitary wave solutions to a singularly perturbed generalized mKdV equation, Appl. Math. Lett., 124, Article 107668 pp. (2022) · Zbl 1479.35214 |
[12] |
Mansour, M. B.A., Traveling wave solutions for a singularly perturbed Burgers-KdV equation, Pramana J. Phys., 73, 799-806 (2009) |
[13] |
Xu, Y.; Du, Z.; Wei, L., Geometric singular perturbation method to the existence and asymptotic behavior of traveling waves for a generalized Burgers-KdV equation, Nonlinear Dynam., 83, 65-73 (2016) · Zbl 1349.37071 |
[14] |
Guo, L.; Zhao, Y., Existence of periodic waves for a perturbed quintic BBM equation, Discrete Cont. Dyn. Sys., 40, 4689-4703 (2020) · Zbl 1445.34065 |
[15] |
Tang, Y.; Xu, W.; Shen, J.; Gao, L., Persistence of solitary wave solutions of singularly perturbed Gardner equation, Chaos Solit. Fract., 37, 532-538 (2008) · Zbl 1143.35359 |
[16] |
Du, Z.; Li, J.; Li, X., The existence of solitary wave solutions of delayed Camassa-Holm equation via a geometric approach, J. Funct. Anal., 275, 4, 988-1007 (2018) · Zbl 1392.35223 |
[17] |
Du, Z.; Qi, Q., The dynamics of traveling waves for a nonlinear Belousov-Zhabotinskii system, J. Differ. Equ., 269, 7214-7230 (2020) · Zbl 1440.35291 |
[18] |
Sun, X.; Zeng, Y.; Yu, P., Analysis and simulation of periodic and solitary waves in nonlinear dispersive-dissipative solids, Commun. Nonlinear Sci. Numer. Simul., 102, Article 105921 pp. (2021) · Zbl 1479.34078 |
[19] |
Zhang, H.; Xia, Y.; N’gbo, P., Global existence and uniqueness of a periodic wave solution of the generalized Burgers-Fisher equation, Appl. Math. Lett., 121, Article 107353 pp. (2021) · Zbl 1475.35103 |
[20] |
Han, M.; Zhu, D., Bifurcation Theory of Differential Equations (1994), China Coal Industry Publishing House: China Coal Industry Publishing House Beijing, (in chinese) |
[21] |
Perko, L. M., Higher order bifurcations of limit cycles, J. Differ. Equ., 154, 339-363 (1999) · Zbl 0926.34033 |
[22] |
Melnikov, V. K., On the stability of the center for the time periodic perturbations, Trans. Moscow Math. Soc., 12, 1-57 (1963) · Zbl 0135.31001 |
[23] |
Han, M., Bifurcation Theory of Limit Cycles (2013), Science Press: Science Press Beijing |
[24] |
Dumortier, F.; Li, C., Perturbations from an elliptic Hamiltonian of degree four. I. Saddle loop and two saddle cycle, J. Differ. Equ., 176, 114-157 (2001) · Zbl 1004.34018 |