Adjoint solutions and superposition principle for linearizable Krichever-Novikov equation

Abstract

Existence of an operator equality for equations connected by nonlocal transformations allowed us to propose a method of finding of a new solution of the initial equation adjoint to its known solution. This approach is used for construction of exact solutions for the linearizable Krichever-Novikov equation and for the corresponding linear equation. The formula of nonlinear nonlocal superposition of solutions for this nonlinear equation is derived and applied to generation of its solutions.