Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A new method to obtain second-order reductions for ordinary differential equations which are polynomial in the derivatives of the dependent variable is presented. The method is applied to obtain reductions and new solutions to several ll-known equations of mathematical physics: a lubrication equation, a thin-film equation, the Zoomeron equation and a family of 5 th - order partial differential equations which includes the Caudrey-Dodd-Gibbon-Sawada-Kotera, Kaup-Kupershmidt, Ito and Lax equations. Some pieces of computer algebra code to derive the reductions are also included.
['J. Ramírez', 'J. L. Romero', 'C. Muriel']
I am writing a research paper on a idea Reductions of PDEs to second order ODEs and symbolic computation
[{"from": "human", "value": "I am writing a research paper on a idea Reductions of PDEs to second order ODEs and symbolic computation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A new method to obtain second-order reductions for ordinary differential equations which are polynomial in the derivatives of the dependent variable is presented. The method is applied to obtain reductions and new solutions to several ll-known equations of mathematical physics: a lubrication equation, a thin-film equation, the Zoomeron equation and a family of 5 th - order partial differential equations which includes the Caudrey-Dodd-Gibbon-Sawada-Kotera, Kaup-Kupershmidt, Ito and Lax equations. Some pieces of computer algebra code to derive the reductions are also included."}]