Solitons | Partial differential equations | Differential geometry | Exactly solvable models

Nonlinear partial differential equation

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. (Wikipedia).

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This video briefly describes the approach to gaining information about the solution to nonlinear differential equations. https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

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From playlist Differential Equations

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From playlist Differential Equations

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From playlist Popular Questions

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From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION

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Linear differential equations: how to solve

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From playlist A second course in university calculus.

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From playlist Engineering Mathematics (UW ME564 and ME565)

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From playlist Numerical Computation spring 2015. Wen Shen. Penn State University.

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From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION

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Nonlinear system | Dispersive partial differential equation | Einstein field equations | Lax pair | Operator (mathematics) | Ricci flow | Separation of variables | Partial differential equation | Soliton | Integrable system | Inverse scattering transform | Calabi conjecture | Euler–Lagrange equation | Navier–Stokes existence and smoothness | Poincaré conjecture | List of nonlinear partial differential equations | Primitive equations | Sobolev space