Partially integrable generalizations of classical integrable models by combination of characteristics method and Hopf-Cole transformation

TL;DR

This paper introduces an integration algorithm combining the characteristics method and Hopf-Cole transformation, enabling partial integration of complex multidimensional nonlinear PDEs like fluid dynamics and KdV generalizations.

Contribution

The paper presents a novel algorithm that merges two classical methods to partially solve a broad class of multidimensional nonlinear PDEs, expanding solution techniques.

Findings

Algorithm effectively integrates certain multidimensional nonlinear PDEs.

Application to fluid dynamics and KdV generalizations demonstrates versatility.

Discussion of solution space richness highlights potential for further research.

Abstract

We represent an integration algorithm combining the characteristics method and Hopf-Cole transformation. This algorithm allows one to partially integrate a large class of multidimensional systems of nonlinear Partial Differential Equations (PDEs). A specific generalization of the equation describing the dynamics of two-dimensional viscous fluid and a generalization of the Korteweg-de Vries equation are examples of such systems. The richness of available solution space for derived nonlinear PDEs is discussed.