加德纳方程（Gardner equation）是数学家C.S.Gardner 在1968年为推广KdV方程而作的非线性偏微分方程。加德纳方程常见于流体力学、等离子物理学和量子场论等领域^[1]

${\displaystyle {\frac {\partial u}{\partial t))+(2au-3bu^{2}){\frac {\partial u}{\partial x))+{\frac {\partial ^{3}u}{\partial x^{3))}=0}$

解析解

加德纳方程有多种行波解^[2]

参考文献

1. ^ Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple p13 Springer
2. ^ Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple p201-202 Springer

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