Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations

TL;DR

This paper derives explicit multi-parameter solutions for the Jimbo-Miwa and Konopelchenko-Dubrovsky equations using advanced methods, enhancing their applicability in physical models despite their complex integrability properties.

Contribution

It introduces novel explicit solutions for these equations via a generalized stable-range method, expanding the solution space for complex integrable systems.

Findings

Obtained explicit solutions with multiple parameters

Enhanced solution applicability to practical models

Demonstrated effectiveness of the generalized stable-range method

Abstract

The Jimbo-Miwa equation is the second equation in the well known KP hierarchy of integrable systems, which is used to describe certain interesting (3+1)-dimensional waves in physics but not pass any of the conventional integrability tests. The Konopelchenko-Dubrovsky equations arose in physics in connection with the nonlinear weaves with a weak dispersion. In this paper, we obtain two families of explicit exact solutions with multiple parameter functions for these equations by using Xu's stable-range method and our logarithmic generalization of the stable-range method. These parameter functions make our solutions more applicable to related practical models and boundary value problems.