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- W255354008 abstract "In this paper new similarity reductions for several physically and mathematically significant, nonlinear partial differential equations are discussed. In particular new reductions and special solutions are presented for the Boussinesq (Bq) and Kadomtsev-Petviashvili (KP) equations $${{u}_{{tt}}} + u{{u}_{{xx}}} + u_{x}^{2} + {{sigma }^{2}}{{u}_{{xxxx}}} = 0,$$ (1) $${{({{u}_{t}} + u{{u}_{x}} + {{u}_{{xxxx}}})}_{x}} + {{sigma }^{2}}{{u}_{{yy}}} = 0,$$ (2) respectively, with σ2 =±1, both of which arise in several physical applications and are completely integrable soliton equations (cf. [1], [2]).KeywordsPartial Differential EquationSimilarity ReductionSpecial SolutionNonlinear Partial Differential EquationOverdetermined SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W255354008 date "1990-01-01" @default.
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- W255354008 title "Examples of Nonclassical Similarity Reductions" @default.
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- W255354008 doi "https://doi.org/10.1007/978-3-642-84039-5_7" @default.
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