Terms Of Wronskian Determinants Research Articles

N-soliton solutions for a (3+1)-dimensional nonlinear evolution equation

Abstract Via Hirota bilinear method and perturbation technique, a more general N-soliton solution with a parameter p for a (3+1)-dimensional nonlinear evolution equation is obtained. And two N-soliton solutions in terms of Wronskian determinant are also presented in the case of p = 1 and p = 3.

A KdV-Type Wronskian Formulation to Generalized KP, BKP and Jimbo–Miwa Equations**Supported by the National Natural Science Foundation of China under Grant No. 11371326

The purpose of this paper is to introduce a class of generalized nonlinear evolution equations, which can be widely applied to describing a variety of phenomena in nonlinear physical science. A KdV-type Wronskian formulation is constructed by employing the Wronskian conditions of the KdV equation. Applications are made for the (3+1)-dimensional generalized KP, BKP and Jimbo–Miwa equations, thereby presenting their Wronskian sufficient conditions. An N-soliton solution in terms of Wronskian determinant is obtained. Under a dimensional reduction, our results yield Wronskian solutions of the KdV equation.

Bäcklund transformation and soliton solutions for two (3+1)-dimensional nonlinear evolution equations

In this paper, two (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear evolution equations (NLEEs) are under investigation by employing the Hirota’s method and symbolic computation. We derive the bilinear form and bilinear Bäcklund transformation (BT) for the two NLEEs. Based on the bilinear form, we obtain the multi-soliton solutions for them. Furthermore, multi-soliton solutions in terms of Wronskian determinant for the first NLEE are constructed, whose validity is verified through direct substitution into the bilinear equations.

Darboux theorems and Wronskian formulas for integrable systems: I. Constrained KP flows

Generalizations of the classical Darboux theorem are established for pseudo-differential scattering operators of the form L = ∑ i=0 N u i∂ i + Σ i=1 m Φ i∂ −1 Ψ i † i . Iteration of the Darboux transformations leads to a gauge transformed operator with coefficients given by Wronskian formulas involving a set of eigenfunctions of L. Nonlinear integrable partial differential equations are associated with the scattering operator L which arise as a symmetry reduction of the multicomponent KP hierarchy. With a suitable linear time evolution for the eigenfunctions the Darboux transformation is used to obtain solutions of the integrable equations in terms of Wronskian determinants.

Soliton solution of three differential-difference equations in wronskian form

The soliton of the differential-difference equations: Toda lattice equation, non-linear lumped self-dual network equations and differential-difference analogue of the Korteweg-de Vries equation are written in terms of wronskian determinants and it is demonstrated how this way of writing the solutions makes the normally very difficult process of verifying the solution, much simpler.