A note on new solitary and similarity class of solutions of a fourth-order non-linear evolution equation
The author analyzes the algebraic properties of solutions of the nonlinear equation \[ \frac{\partial^{2}U}{\partial {t^{2}}}+\frac{\partial^{4}U}{\partial{x^{3}}\partial t}+ 3\frac{\partial^{2}U}{\partial{x^{2}}}\frac{\partial^{2}U}{\partial x \partial t}=0,\quad t>0 \] using the properties of the ordinary differential equation obtained by the transform \[ U(x,t)=f(\xi),\quad \text{with} \quad \xi=x-\lambda t. \]
scientific article; zbMATH DE number 5321670