Abstract CONTENTS § 1. Introduction § 2. Definition of generalized functions § 3. Properties
of generalized functions § 4. Weak equality § 5. Generalized functions and boundary-value …

We introduce a new definition of aδ-shock wave type solution for a class of systems of
conservation laws in the one-dimensional case. The weak asymptotics method developed …

CONTENTS Introduction. Examples of non-standard characteristics. Statement of the
general problem Chapter I. Characteristics of linear equations and equations with a non …

The physics of extended systems is a topic of great interest for the experimentalist and the
theoretician alike. There exists a large literature on this subject in which solutions …

For two classes of hyperbolic systems of conservation laws new definitions of a $\delta $-
shock wave type solution are introduced. These two definitions give natural generalizations …

In the present book the reader will find a review of methods for constructing a certain class of
asymptotic solutions, which we call self-stabilizing solutions. This class includes solitons …

We consider propagation of solitons along large-scale background waves in the generalized
Korteweg–de Vries (gKdV) equation theory when the width of the soliton is much smaller …

Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a
variety of “unusual” physical phenomena by means of nonlinear differential equations …

SB Leble's book deals with nonlinear waves and their propagation in metallic and dielectric
waveguides and media with stratification. The underlying nonlinear evolution equations …

In this article generalized solutions to two model equations describing nonlinear dispersive
waves are studied. The solutions are found in certain algebras of new generalized functions …