کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8898985 1631506 2018 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
ترجمه فارسی عنوان
راه حل های یکسان برای معادلات دیفرانسیل غیر انتگرال نامتعارفی از طریق فرم های هیولا هیلیتا
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u=2(ln⁡f)x and u=2(ln⁡f)xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 4, 15 February 2018, Pages 2633-2659
نویسندگان
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