NDLI: Extended Rotation and Scaling Groups for Nonlinear Evolution Equations

Content Provider	Springer Nature Link
Author	Estevez, P. G. Qu, C.
Copyright Year	2003
Abstract	A (1+1)-dimensional nonlinear evolution equation is invariant under the rotation group if it is invariant under the infinitesimal generator V = x∂$_{ u }$ − u∂$_{ x }$. Then the solution satisfies the condition u $_{x}$ = −x/u. For equations that do not admit the rotation group, we provide an extension of the rotation group. The corresponding exact solution can be constructed via the invariant set R $_{0}$ = {u: u $_{x}$ = xF(u)} of a contact first-order differential structure, where F is a smooth function to be determined. The time evolution on R $_{0}$ is shown to be governed by a first-order dynamical system. We introduce an extension of the scaling groups characterized by an invariant set $$\tilde S_0 $$ that depends on two constants ∈ and n ≠ 1. When ∈ = 0, it reduces to the invariant set S $_{0}$ introduced by Galaktionov. We also introduce a generalization of both the scaling and rotation groups, which is described by an invariant set E $_{0}$ with parameters a and b. When a = 0 or b = 0, it respectively reduces to R $_{0}$ or S $_{0}$. These approaches are used to obtain exact solutions and reductions of dynamical systems of nonlinear evolution equations.
Starting Page	1419
Ending Page	1429
Page Count	11
File Format	PDF
ISSN	00405779
Journal	Theoretical and Mathematical Physics
Volume Number	137
Issue Number	1
e-ISSN	15739333
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2003-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Applications of Mathematics Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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