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On the solution of evolution p-Laplace equation with memory term and unknown boundary Dirichlet condition
In the present paper, we are interested in investigating a classe of nonlinear parabolic integro-differential equation with unknown flux on the part...
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Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method
We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e.... -
Index
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Symmetries of Discrete Systems
In this series of lectures, we review the application of Lie point symmetries, and their generalizations, to the study of difference equations. The... -
Discrete Painlevé Equations: A Review
We present a review of what is current knowledge about discrete Painlevé equations. We start with a historical introduction which explains how the... -
Bilinear Formalism in Soliton Theory
A brief survey of the bilinear formalism discovered by Hirota is given. First, the procedure to obtain soliton solutions of nonlinear evolution... -
Sato Theory and Transformation Groups. A Unified Approach to Integrable Systems
More than 20 years ago, it was discovered that the solutions of the Kadomtsev-Petviashvili (KP) hierarchy constitute an infinite-dimensional... -
Ultradiscrete Systems (Cellular Automata)
Ultradiscretization is a limiting procedure which allows one to obtain a cellular automaton (CA) from continuous equations. Using this method, we can... -
Time in Science: Reversibility vs. Irreversibility
To discuss properly the question of irreversibility one needs to make a careful distinction between reversibility of the equations of motion and the... -
Nonlinear Waves, Solitons, and IST
These lectures are written for a wide audience with diverse backgrounds. The subject is approached from a general perspective and overly detailed... -
Integrability – and How to Detect It
We present a physicist’s approach to integrability and its detection. Starting from specific examples we present a working definition of what is... -
Introduction
Nonlinear systems model all but the simplest physical phenomena. In the classical theory, the tools of Poisson geometry appear in an essential way,... -
A. Proof of Thm. 4.34
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Exact solutions of nonlinear partial differential equations by singularity analysis
Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with... -
Hirota bilinear method for nonlinear evolution equations
The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples...