非线性偏微分方程的在物理学、气动力学、流体力学、大气物理、海洋物理、爆炸物理、化学、生理学、生物学、生态学等领域都有重要的应用。非线性偏微分方程的研究，是当前微分方程研究的中心。求解非线性偏微分方程比求解线性偏微分方程，难度大的多，大多数非线性偏微分方程只能依靠数值解法。但多年来数学家们发现了一些行之有效的求解非线性偏微分方程的构造性解法，如反散射法、达布变换法，tanh、雅可比函数展开法等，得出非线性偏微分方程的解析解。解非线性偏微分方程，过程复杂，多数得力于Maple、Mathematica、Matlab等商用计算机代数系统。

In mathematics and physics, nonlinear partial differential equations are (as their name suggests) partial differential equations 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: there are almost no general techniques that work for all such equations, and usually each individual equation has to be studied as a separate problem.