On integration of multidimensional generalizations of classical $C$- and $S$-integrable nonlinear partial differential equations

TL;DR

This paper introduces a novel integration method for constructing solutions to multidimensional generalizations of classical $C$- and $S$-integrable nonlinear PDEs, expanding the scope of integrable systems.

Contribution

A new technique for solving multidimensional integrable PDEs is developed, enabling the construction of a broad class of particular solutions for generalized equations.

Findings

Derived generalizations of classical $C$- and $S$-integrable PDEs

Constructed particular solutions for multidimensional equations

Presented examples including second order PDEs

Abstract

We develop a new integration technique allowing one to construct a rich manifold of particular solutions to multidimensional generalizations of classical $C$- and $S$-integrable Partial Differential Equations (PDEs). Generalizations of (1+1)-dimensional $C$-integrable and (2+1)-dimensional $S$-integrable $N$-wave equations are derived among examples. Examples of multidimensional second order PDEs are represented as well.