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Li, Zhi-Qiang; Tian, Shou-Fu

A hierarchy of nonlocal nonlinear evolution equations and \(\overline{\partial} \)-dressing method. (English) Zbl 1479.35745

Appl. Math. Lett. 120, Article ID 107254, 8 p. (2021).
Summary: Starting from the matrix \(\overline{\partial}\) problem, the dressing method is employed to investigate the nonlocal nonlinear evolution equations. A hierarchy of nonlocal nonlinear evolution equations associated with \(2 \times 2\) matrix problem, which contains the nonlocal extended modified Korteweg-de Vries (emKdV) equation, is derived via using recursive operator for the first time. Finally, via selecting a proper spectral transformation matrix, the \(N\)-soliton solutions of the nonlocal emKdV equation are constructed based on the matrix \(\overline{\partial}\) problem.

Cited in 7 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems

Keywords:

nonlocal extended modified Korteweg-de Vries equation; \( \overline{\partial} \)-dressing method; recursive operator; \(N\)-soliton solution
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Full Text: DOI

References:

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