Non-linearity and self-similarity: patterns and clusters

Andrei Ludu

Non-linearity and self-similarity: patterns and clusters

Embry-Riddle Aeronautical University

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a qualitative similarity analysis, which yields relations between the geometry and kinematics of traveling localized solutions, associated to certain non-linear equations. This method predicts the existence of solitons, compactons, doublets, triplets, as well as other non-linear patterns. A finite supported wavelet-like frame is constructed in terms of compacton kink–antikink (KAK) solutions.

Original language	American English
Journal	Mathematics and Computers in Simulation
Volume	55
State	Published - 2001
Externally published	Yes

Keywords

Solitons
wavelets
Hamiltonian system
compactons
clusters
nonlinearity
nonlinear partial differential equations
traveling waves

Disciplines

Fluid Dynamics
Harmonic Analysis and Representation
Non-linear Dynamics
Partial Differential Equations
Physics

Cite this

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title = "Non-linearity and self-similarity: patterns and clusters",

abstract = "We introduce a qualitative similarity analysis, which yields relations between the geometry and kinematics of traveling localized solutions, associated to certain non-linear equations. This method predicts the existence of solitons, compactons, doublets, triplets, as well as other non-linear patterns. A finite supported wavelet-like frame is constructed in terms of compacton kink–antikink (KAK) solutions.",

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KW - Solitons

KW - wavelets

KW - Hamiltonian system

KW - compactons

KW - clusters

KW - nonlinearity

KW - nonlinear partial differential equations

KW - traveling waves

M3 - Article

VL - 55

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

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