On the equivalence of different approaches for generating multisoliton solutions of the KPII equation

Abstract

The unexpectedly rich structure of the multisoliton solutions of the KPII equation has been explored by using different approaches, running from dressing method to twisting transformations and to the tau-function formulation. All these approaches proved to be useful in order to display different properties of these solutions and their related Jost solutions. The aim of this paper is to establish the explicit formulae relating all these approaches. In addition some hidden invariance properties of these multisoliton solutions are discussed.

References in corpus (4)

• Classification of the line-soliton solutions of KPII
• On the equivalence of different approaches for generating multisoliton solutions of the KPII equation
• Building extended resolvent of heat operator via twisting transformations
• Soliton solutions of the KP equation and application to shallow water waves

Cited by in corpus (10)

• On the equivalence of different approaches for generating multisoliton solutions of the KPII equation
• Vertex dynamics in multi-soliton solutions of Kadomtsev-Petviashvili II equation
• Integrability, exact reductions and special solutions of the KP-Whitham equations
• Heat operator with pure soliton potential: properties of Jost and dual Jost solutions
• The direct scattering problem for perturbed Kadomtsev-Petviashvili multi line solitons
• The direct scattering problem for the perturbed $\text{Gr}(1,2{)}_{\ge 0}$ Kadomtsev-Petviashvili solitons
• Extended resolvent of heat operator with multisoliton potential
• On soliton solutions and soliton interactions of Kulish-Sklyanin and Hirota-Ohta systems
• Two-dimensional reductions of the Whitham modulation system for the Kadomtsev-Petviashvili equation
• IST of KPII equation for perturbed multisoliton solutions