Lie-Bäcklund-type analysis have been performed for one nonlinear partial differential equation, which is somewhat different from those usually studied. We consider the KdV equation with an explicit x dependence. In this case we show the form of symmetry generators and find the ordinary differential equation connected with them having no movable critical points. This clearly extends the class of equations analysed by Ablowitz.
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Chowdhury, A.R., Chowdhury, K.R. & Mahato, G. Lie-Bäcklund transformation and ordinary differential equations associated with some nonlinear equations. Lett Math Phys 6, 423–428 (1982). https://doi.org/10.1007/BF00405861
- Ordinary Differential Equation
- Solitary Wave
- Nonlinear Partial Differential Equation
- Solitary Wave Solution