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- ...fferential equation topics]] and [[List of nonlinear ordinary differential equations]]. ...dot\frac{\partial f_i}{\partial \mathbf{p}_i} = \left(\frac{\partial f_i}{\partial t} \right)_\mathrm{coll},</math> ...23 KB (3,497 words) - 10:50, 27 January 2025
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- ...Polyanin, Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p540-542 CRC PRESS</ref> ...hs William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press ...1 KB (143 words) - 04:24, 18 January 2024
- ....<ref>LI Zhibing Traveling wave solution of nonlinear mathematical physics equations SCIENCEP 2008(李志斌编著 《非线性数学物理方程的行波解》 科学出版社 2008)</ref> * [[List of nonlinear partial differential equations]] ...1 KB (149 words) - 17:26, 6 January 2024
- ...ons''' are an [[integrable system]] of two coupled [[nonlinear]] [[partial differential equation]]s proposed by [[Vladimir Drinfeld]] and Vladimir Sokolov, and ind &\frac{\partial u}{\partial t}+3v\frac{\partial v}{\partial x}=0\\[5pt] ...833 bytes (101 words) - 05:57, 13 June 2024
- ...on]]s''' are a set of two coupled [[Nonlinear system|nonlinear]] [[partial differential equation]]s:<ref>阎振亚著 《复杂非线性波的构造性理论及其应用》 第65页 科学出版社 2007年(in Chinese, SCIE ...ths, William E. Shiesser, "Traveling Wave Analysis of Partial Differential Equations", p. 135 ''Academic Press'' ...1 KB (154 words) - 16:56, 6 August 2021
- ...olyanin, Valentin F. Zaitsev, ''Handbook of Nonlinear Partial Differential Equations'', equation # 5.1.10.3. second edition p. 212 CRC PRESS</ref> [[Category:Nonlinear partial differential equations]] ...652 bytes (80 words) - 00:52, 17 May 2024
- ....<ref>Li Zhibing Traveling Wave Solution of Nonlinear Mathematical Physics equations SCIENCEP 2008(李志斌编著 《非线性数学物理方程的行波解》 页 科学出版社 2008)</ref> ...'x'', ''y'', ''t'', then we denote <math> \frac{\partial^3 U}{\partial t\,\partial y^2} </math> by ''U''<sub>''tyy''</sub>, and so on. With that notation, the ...2 KB (202 words) - 08:47, 13 December 2018
- The '''Dodd–Bullough–Mikhailov equation''' is a [[nonlinear partial differential equation]] introduced by Roger Dodd, [[Robin Bullough]], and Alexander Mikh Dodd-Bullough equations,” Chaos, Solitons and Fractals, vol. 25, no. 1, pp. 55–63, 2005.</ref> ...2 KB (196 words) - 09:25, 18 November 2024
- ...aves]] when the third-order contributions are small. The term may refer to equations of the form : <math>u_{t}+\alpha u_{xxx}+\beta u_{xxxxx} = \frac {\partial} {\partial x} f(u, u_{x}, u_{xx})</math> ...1 KB (223 words) - 18:48, 26 January 2025
- {{Short description|Solvable form of differential equation}} {{Differential equations}} ...3 KB (429 words) - 21:14, 8 February 2025
- ...dV) equation''' is an [[Integrable system|integrable]] nonlinear [[partial differential equation]]:{{sfn | Polyanin | Zaitsev | 2003}} ...ser | first2=W. E. | title=Traveling Wave Analysis of Partial Differential Equations | publisher=Academic Press | publication-place=Amsterdam; Boston | year=201 ...1 KB (142 words) - 04:02, 3 July 2024
- The '''Gardner equation''' is an [[integrable]] [[nonlinear partial differential equation]] introduced by the mathematician [[Clifford Gardner]] in 1968 to ...varepsilon^2 u^2 + 6u) \frac{\partial u}{\partial x }+\frac{\partial^3 u}{\partial x^3}=0,</math> ...1 KB (142 words) - 15:09, 16 January 2025
- ...<ref>Li Zhibing Traveling Wave Solutions of Nonlinear Mathematical Physics Equations P140, SCIENCEP 2008 (李志斌编著 《非线性数学物理方程的行波解》 140页 科学出版社 2008)</ref> ...n 1976.<ref>Hirota, Ryogo; Satsuma, Junkichi, N-Soliton Solutions of Model Equations for Shallow Water Waves, Journal of the Physical Society of Japan, Volume 4 ...2 KB (292 words) - 23:27, 27 January 2025
- '''Ehrenfest equations''' (named after [[Paul Ehrenfest]]) are equations which describe changes in [[specific heat capacity]] and derivatives of [[s ...of [[temperature]] and [[pressure]], then its [[differential of a function|differential]] is: ...3 KB (480 words) - 23:20, 12 February 2024
- {{Short description|Nonlinear partial differential equation}} The '''Korteweg–de Vries–Burgers equation''' is a nonlinear [[partial differential equation]]: ...1 KB (191 words) - 11:14, 26 February 2025
- ...concept of [[ordinary differential equation]] in mathematics defined as [[differential inclusion]] for non-uniform upper [[hemicontinuity]] [[convex set]] with [[ == First order fuzzy differential equation == ...4 KB (476 words) - 05:09, 7 July 2024
- ...l coordinates <math>y_1, \dots, y_n</math> such that <math>X = \partial / \partial y_1</math> in a neighborhood of a point where <math>X</math> is nonzero. Th The [[Frobenius theorem (differential topology)|Frobenius theorem]] in differential geometry can be considered as a higher-dimensional generalization of this t ...2 KB (335 words) - 10:38, 9 January 2025
- ...2=Olech |title=On Global Asymptotic Stability of Solutions of Differential Equations |journal=[[Transactions of the American Mathematical Society]] |volume=104 The differential equations <math>\mathbf{\dot{x}} = f ( \mathbf{x} )</math>, <math>\mathbf{x} = [ x_1 ...2 KB (281 words) - 07:59, 14 June 2024
- ...tial algebraic equation (PDAE)''' set is an incomplete system of [[partial differential equation]]s that is closed with a set of [[algebraic equation]]s. ...y, \frac{\partial y_i}{\partial x_j}, \frac{\partial^2 y_i}{\partial x_j \partial x_k}, \ldots, \mathbf z \right),</math> ...3 KB (402 words) - 02:07, 7 December 2024
- ...ew gradient can be defined using complex analysis and the [[Cauchy–Riemann equations]]. and from the [[Cauchy–Riemann equations]], it is derived that ...1 KB (218 words) - 23:20, 20 January 2016
- ...ntial equation]] devised by [[Gheorghe Țițeica]] in 1907 in the study of [[differential geometry]], describing surfaces of constant [[affine curvature]].<ref>{{cit ...=Polyanin|first=Andrei D.|title=Handbook of Nonlinear Partial Differential Equations|last2=Zaitsev|first2=Valentin F.|date=2016-04-19|publisher=[[Chapman & Hall ...3 KB (359 words) - 04:06, 18 January 2024