Darboux Transformation and Variable Separation Approach: the Nizhnik-Novikov-Veselov equation

Abstract

Darboux transformation is developed to systematically find variable separation solutions for the Nizhnik-Novikov-Veselov equation. Starting from a seed solution with some arbitrary functions, the once Darboux transformation yields the variable separable solutions which can be obtained from the truncated Painlevé analysis and the twice Darboux transformation leads to some new variable separable solutions which are the generalization of the known results obtained by using a guess ansatz to solve the generalized trilinear equation.

12 pages, 6 figures

References in corpus (4)

• Folded solitary waves and Foldons in 2+1 dimensions
• Exact solution of d=1 Kazakov-Migdal induced gauge theory
• Darboux transformation for the modified Veselov-Novikov equation
• Relation between the solitons of Yang-Mills-Higgs fields in 2+1 dimensional Minkowski space-time and anti-de Sitter space-time

Cited by in corpus (8)

• Two-dimensional rational solitons and their blow-up via the Moutard transformation
• The Gould-Hopper Polynomials in the Novikov-Veselov equation
• On the N-Solitons Solutions in the Novikov-Veselov Equation
• Mach-Type Soliton in the Novikov-Veselov Equation
• Darboux-Moutard transformations and Poincare-Steklov operators
• The Moutard transformation and two-dimensional multi-point delta-type potentials
• Faddeev eigenfunctions for two-dimensional Schrodinger operators via the Moutard transformation
• Relation between hyperbolic Nizhnik-Novikov-Veselov equation and stationary Davey-Stewartson II equation