Dressing method based on homogeneous Fredholm equation: quasilinear PDEs in multidimensions

Abstract

In this paper we develop a dressing method for constructing and solving some classes of matrix quasi-linear Partial Differential Equations (PDEs) in arbitrary dimensions. This method is based on a homogeneous integral equation with a nontrivial kernel, which allows one to reduce the nonlinear PDEs to systems of non-differential (algebraic or transcendental) equations for the unknown fields. In the simplest examples, the above dressing scheme captures matrix equations integrated by the characteristics method and nonlinear PDEs associated with matrix Hopf-Cole transformations.

31 pages

References in corpus (3)

• Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
• On the dbar-dressing method applicable to heavenly equation
• Partially integrable systems in multidimensions by a variant of the dressing method. 1

Cited by in corpus (4)

• Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation
• On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields
• On integration of multidimensional generalizations of classical $C$- and $S$-integrable nonlinear partial differential equations
• New multidimensional partially integrable generalization of S-integrable N-wave equation