Abstract
The (2 + 1)-dimensional Korteweg de Vries (KdV) equation, which was first derived by Boiti et al., has been studied by various distinct methods. It is known that this (2 + 1)-dimensional KdV equation has rich solutions, such as multi-soliton solutions and dromion solutions. In the present article, a unified representation of its N-soliton solution is given by means of pfaffian. We’ll show that this (2 + 1)-dimensional KdV equation is nothing but the Plucker identity when its τ-function is given by pfaffian.
Highlights
The solitary wave, so-called because it often occurs as a single entity and is localized, was first observed by J
We’ll show that this (2 + 1)-dimensional Korteweg de Vries (KdV) equation is nothing but the Plücker identity when its τ-function is given by pfaffian
It is known that many nonlinear evolution equations have soliton solutions, such as the Korteweg de Vries equation, the Sin-Gordon equation, the nonlinear Schrödinger equation, the Kadomtsev-Petviashvili equation, the Davey-Stewartson equation, etc
Summary
The solitary wave, so-called because it often occurs as a single entity and is localized, was first observed by J. In order to study the property of nonlinear evolution equations, methods are developed to derive solitary wave solution or soliton solution to nonlinear evolution equations. Having soliton solutions is one of the basic integrable properties of nonlinear evolution equations. ∂x ∂y which was first derived by Boiti et al by using the idea of the weak Lax pair [10] This system can be obtained from the inner parameter-dependent symmetry constraint of the KP equation [11]. Given a nonlinear evolution equation, if it has 3-soliton solution, this equation is of great possibility of having N-soliton ( 3 ≤ N ) solution. We first review some properties of pfaffian
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