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Initial-value problems for evolutionary partial differential equations and higher-order conditional symmetries
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Institute of Mathematics, 3 Tereshchenkivska Street, 252004 Kyiv, Ukraine.
2001 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, Vol. 42, no 1, 376-389 p.Article in journal (Refereed) Published
Abstract [en]

We suggest a new approach to the problem of dimensional reduction of initial/ boundary value problems for evolution equations in one spatial variable. The approach is based on higher-order (generalized) conditional symmetries of the equations involved. It is shown that reducibility of an initial value problem for an evolution equation to a Cauchy problem for a system of ordinary differential equations can be fully characterized in terms of conditional symmetries which leave invariant the equation in question. We also give some examples of the solution of initial value problems for second- and third-order nonlinear differential equations by reduction by their conditional symmetries. We give a systematic classification of general second-order partial differential equations admitting second-order conditional symmetries, based on Lie's classification of invariant second-order ordinary differential equations. This yields five classes of principally new initial value problems for nonlinear evolution equations which admit no Lie symmetries and are reducible via second-order conditional symmetries. © 2001 American Institute of Physics.

Place, publisher, year, edition, pages
2001. Vol. 42, no 1, 376-389 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-47490DOI: 10.1063/1.1330199OAI: diva2:268386
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-13

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Basarab-Horwath, Peter
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ReferencesLink to record
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