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In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist that work for all such equations, and usually each individual equation has to be studied as a separate problem.

Attributes	Values
rdfs:label	Nonlinear partial differential equation (en) 非线性偏微分方程 (zh)
rdfs:comment	非线性偏微分方程起源於各種應用科學中，如固體力學，流體力學，聲學，非線性光學，等離子體物理學，量子場論等學科。函數關係 F=0 是一個廣義的偏微分方程，如果 u，v 是此微分方程的兩個解，而（au+bv) 也是此微分方程的解，則此偏微分方程稱為線性偏微分方程，否則稱為非線性偏微分方程。 (zh) In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist that work for all such equations, and usually each individual equation has to be studied as a separate problem. (en)
dcterms:subject	Differential geometry Exactly solvable models Solitons Partial differential equations
Wikipage page ID	16678376 (xsd:integer)
Wikipage revision ID	1117518387 (xsd:integer)
Link from a Wikipage to another Wikipage	Ricci flow Richard S. Hamilton Integrable system Inverse scattering transform List of nonlinear partial differential equations Weather prediction Differential geometry Operator (mathematics) Einstein field equations Exactly solvable models Solitons Calabi conjecture Sobolev space Dispersive partial differential equation Lax pair Euler–Lagrange equation Partial differential equation Primitive equations Grigori Perelman Partial differential equations Monge–Ampere equation Poincaré conjecture Korteweg–de Vries equation Separation of variables Soliton Navier–Stokes existence and smoothness Navier–Stokes equation Nonlinear system Yang–Mills equation Millennium Prize problems Gauge group Seiberg–Witten equations
Link from a Wikipage to an external page	http://eqworld.ipmnet.ru/ https://web.archive.org/web/20060812140140/http:/tosio.math.toronto.edu/wiki/index.php/Main_Page http://www.primat.mephi.ru/wiki/ http://personal.riverusers.com/~rover/typosens.html https://books.google.com/books%3Fid=YD4PL0GZgOcC&q=%22nonlinear+partial%22 https://web.archive.org/web/20181212023755/https:/primat.mephi.ru/wiki/
sameAs	Nonlinear partial differential equation Nonlinear partial differential equation Nonlinear partial differential equation
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Citation dbt:Further dbt:Main_article dbt:Reflist dbt:Webarchive dbt:Differential_equations
date	2018-12-12 (xsd:date)
first	S.I. (en)
id	N/n067170 (en)
last	Pokhozhaev (en)
title	Non-linear partial differential equation (en)
url	https://web.archive.org/web/20181212023755/https:/primat.mephi.ru/wiki/
has abstract	In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist that work for all such equations, and usually each individual equation has to be studied as a separate problem. The distinction between a linear and a nonlinear partial differential equation is usually made in terms of the properties of the operator that defines the PDE itself. (en) 非线性偏微分方程起源於各種應用科學中，如固體力學，流體力學，聲學，非線性光學，等離子體物理學，量子場論等學科。函數關係 F=0 是一個廣義的偏微分方程，如果 u，v 是此微分方程的兩個解，而（au+bv) 也是此微分方程的解，則此偏微分方程稱為線性偏微分方程，否則稱為非線性偏微分方程。 (zh)
prov:wasDerivedFrom	wikipedia-en:Nonlinear_partial_differential_equation?oldid=1117518387&ns=0
page length (characters) of wiki page	8677 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Nonlinear_partial_differential_equation
is rdfs:seeAlso of	Partial differential equation
is Link from a Wikipage to another Wikipage of	Non-linear partial differential equation Nonlinear PDE Nonlinear Partial Differential Equations Benoit Perthame David Benney John von Neumann Index of physics articles (N) List of nonlinear partial differential equations List of partial differential equation topics Robert R. Jensen Mathematical Institute, University of Oxford Estevez–Mansfield–Clarkson equation Sun-Yung Alice Chang Generalized Korteweg–De Vries equation Mónica Clapp Continuity equation Andrea Bertozzi Andrea R. Nahmod Luis Caffarelli Halil Mete Soner Stuart S. Antman Walter Craig (mathematician) Dodd–Bullough–Mikhailov equation Gardner equation Sedleian Professor of Natural Philosophy Edriss Titi Finite difference method Fokas method Partial differential equation Hirota–Satsuma equation

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