Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation
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Publication:4592907
DOI10.1063/1.5005611zbMath1380.37132OpenAlexW2761690065MaRDI QIDQ4592907
Li-Yuan Ma, Zuo-nong Zhu, Shou-feng Shen
Publication date: 9 November 2017
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.5005611
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Interaction properties of complex modified Korteweg-de Vries (mKdV) solitons
- Stability of periodic traveling waves for complex modified Korteweg-de Vries equation
- A note on the NLS and the Schrödinger flow of maps
- Stability of a solution of the form of a solitary wave for a nonlinear complex modified Korteweg-de Vries equation
- Numerical simulations of the complex modified Korteweg-de Vries equation
- Numerical homoclinic instabilities and the complex modified Korteweg-de Vries equation
- On a nonlocal modified Korteweg-de Vries equation: integrability, Darboux transformation and soliton solutions
- Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform
- Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
- Nonlocal nonlinear Schrödinger equation and its discrete version: Soliton solutions and gauge equivalence
- Gauge equivalence of sigma models with non-compact Grassmannian manifolds
- A numerical and theoretical study of certain nonlinear wave phenomena
- Integrable Nonlocal Nonlinear Equations
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