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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
- ...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
- ...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
- ...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
- ....<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
- {{distinguish|text=[[Gardner's relation]], a nonlinear equation in rock physics}} The '''Gardner equation''' is an [[integrable]] [[nonlinear partial differential equation]] introduced by the mathematician [[Clifford Gardner]] in 1968 to ...1 KB (142 words) - 15:09, 16 January 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
- ...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|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
- ...<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
- ...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
- ...lentin F. |last2=Zaitsev |title=Handbook of Nonlinear Partial Differential Equations |date=28 October 2002 |edition=Second |page=891 |publisher=CRC Press |isbn= [[Category:Nonlinear partial differential equations]] ...2 KB (225 words) - 09:17, 10 August 2021
- ...u.ac.ir/article_16069.html |journal=Computational Methods for Differential Equations |volume=11 |issue=4 |pages=803–810}}</ref> [[Category:Nonlinear partial differential equations]] ...2 KB (266 words) - 00:26, 28 January 2025
- {{short description|Group of differential equations}} ...n |first=E. R. |date=1941 |title=Notes on Systems of Ordinary Differential Equations |url=https://www.jstor.org/stable/2371531 |journal=American Journal of Math ...7 KB (1,036 words) - 16:22, 3 February 2025
- ...olyanin, Valentin F. Zaitsev, ''Handbook of Nonlinear Partial Differential Equations'', second edition, p. 764 CRC PRESS</ref> In its simplest form, in two dime ...i Tsarev in 1996,<ref>J. Gibbons and S.P. Tsarev, Reductions of the Benney Equations, ...4 KB (591 words) - 23:14, 26 February 2021
- ...|first1=A. |title=A first course in the numerical analysis of differential equations |date=2009 |publisher=Cambridge Texts in Applied Mathematics, Cambridge Uni X_{0, T}^{Y_{0}} - Y_{T} = \int_{0}^{T} \left( \frac{\partial}{\partial x} X_{r, T}^{Y_{s}} \right) \left( \mu(r, Y_{r}) - \frac{d}{dr} Y_{r} \righ ...3 KB (536 words) - 20:07, 17 January 2025
- ...date=2016-05-14|title=Numerical methods for the 2-Hessian elliptic partial differential equation|url=http://dx.doi.org/10.1093/imanum/drw007|journal=IMA Journal of ...an be understood as simply eigenvalue equations acted upon by the Hessian differential operator. Special cases include the [[Monge–Ampère equation]]<ref>{{citatio ...4 KB (548 words) - 17:55, 23 December 2023
- ...al kind of [[Parabolic partial differential equation|parabolic]] [[partial differential equation]]s (PDEs) with a quadratic nonlinearity into a [[Heat equation|lin ...isfy <math>a\phi'' + b\phi' = 0</math>. Then we may transform the original nonlinear PDE into the canonical [[heat equation]] by using the transformation: ...4 KB (588 words) - 16:36, 18 December 2024