N-soliton solution of a combined pKP-BKP equation

In this paper, via the limit technique of long wave, the N-order rational solution of the (2+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is derived from the N-soliton solution. In particular, the bright–dark M-lump solution can be obtained from resulting N-order rational solution. This kind of lump wave in BKP equation exhibits the one-peak-one-valley structure which is different from that in KPI equation. In addition, graphical illustration presents the collision dynamics of multi-bright–dark lump waves.

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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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On the Exact Solutions of Two (3+1)-Dimensional Nonlinear Differential Equations

Journal of Function Spaces ◽

10.1155/2020/5740310 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Fanning Meng ◽

Yongyi Gu

Keyword(s):

Differential Equations ◽

Exact Solutions ◽

Shallow Water ◽

Traveling Wave ◽

Nonlinear Differential Equations ◽

Complex Method ◽

Meromorphic Solutions ◽

Complex Differential Equations ◽

Bkp Equation

In this article, exact solutions of two (3+1)-dimensional nonlinear differential equations are derived by using the complex method. We change the (3+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation and generalized shallow water (gSW) equation into the complex differential equations by applying traveling wave transform and show that meromorphic solutions of these complex differential equations belong to class W, and then, we get exact solutions of these two (3+1)-dimensional equations.

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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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