Soliton Solution for Discrete Hirota Equation*

In this paper, we propose a new semidiscrete Hirota equation which yields the Hirota equation in the continuum limit. We focus on the topic of how the discrete space step δ affects the simulation for the soliton solution to the Hirota equation. The Darboux transformation and explicit solution for the semidiscrete Hirota equation are constructed. We show that the continuum limit for the semidiscrete Hirota equation, including the Lax pair, the Darboux transformation and the explicit solution, yields the corresponding results for the Hirota equation as δ → 0 .

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The Modified Coupled Hirota Equation: Riemann-Hilbert Approach and N-Soliton Solutions

Abstract and Applied Analysis ◽

10.1155/2019/8342876 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10

Author(s):

Siqi Xu

Keyword(s):

Soliton Solution ◽

Initial Value Problem ◽

Soliton Solutions ◽

Compact Form ◽

Initial Value ◽

Hirota Equation ◽

Dynamical Behaviors

The Cauchy initial value problem of the modified coupled Hirota equation is studied in the framework of Riemann-Hilbert approach. The N-soliton solutions are given in a compact form as a ratio of (N+1)×(N+1) determinant and N×N determinant, and the dynamical behaviors of the single-soliton solution are displayed graphically.

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The Complex Hamiltonian Systems and Quasi-periodic Solutions in the Hirota Equation

Journal of Nonlinear Mathematical Physics ◽

10.2991/jnmp.k.200922.010 ◽

2020 ◽

Author(s):

Jinbing Chen ◽

Rong Tong

Keyword(s):

Periodic Solutions ◽

Hamiltonian Systems ◽

Hirota Equation

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Integrable Models

10.1093/oso/9780198805021.003.0009 ◽

2018 ◽

Author(s):

S. G. Rajeev

Keyword(s):

Fluid Mechanics ◽

Soliton Solution ◽

Water Waves ◽

Heisenberg Model ◽

Kdv Equation ◽

Short Review ◽

Lax Pair ◽

Shallow Water Waves ◽

Initial Value ◽

The Kdv Equation

Some exceptional situations in fluid mechanics can be modeled by equations that are analytically solvable. The most famous example is the Korteweg–de Vries (KdV) equation for shallow water waves in a channel. The exact soliton solution of this equation is derived. The Lax pair formalism for solving the general initial value problem is outlined. Two hamiltonian formalisms for the KdV equation (Fadeev–Zakharov and Magri) are explained. Then a short review of the geometry of curves (Frenet–Serret equations) is given. They are used to derive a remarkably simple equation for the propagation of a kink along a vortex filament. This equation of Hasimoto has surprising connections to the nonlinear Schrödinger equation and to the Heisenberg model of ferromagnetism. An exact soliton solution is found.

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Dark soliton solution of Sasa-Satsuma equation

10.1063/1.3367022 ◽

2010 ◽

Cited By ~ 10

Author(s):

Y. Ohta ◽

Wen Xiu Ma ◽

Xing-biao Hu ◽

Qingping Liu

Keyword(s):

Soliton Solution ◽

Dark Soliton

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The Evolutionary Properties on Solitary Solutions of Nonlinear Evolution Equations

Advances in Mathematical Physics ◽

10.1155/2017/5460216 ◽

2017 ◽

Vol 2017 ◽

pp. 1-6

Author(s):

Wenxia Chen ◽

Danping Ding ◽

Xiaoyan Deng ◽

Gang Xu

Keyword(s):

Soliton Solution ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Soliton Solutions ◽

Nonlinear Evolution Equations ◽

Evolution Process ◽

Solution Curve ◽

Solitary Solutions ◽

Basic Calculus

The evolution process of four class soliton solutions is investigated by basic calculus theory. For any given x, we describe the special curvature evolution following time t for the curve of soliton solution and also study the fluctuation of solution curve.

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