Take a look at: Valls, C. Nonlinear Differ. Equ. Appl. (2017) 24: 25. https://doi.org/10.1007/s00030-017-0450-1 Basically this is for a chemical reaction and it is second order in displacement and first order in time, but is non-linear. So this is more general than say the quantum mechanical traveling wave for an electron etc.

Thank you dear professor

Hello,

Links:-

Article Algebraic traveling waves for some family of reaction-diffus...

attached papers.

Thanks,

Thank you very much for your kind courtesy Prof. Smrity Dwivedi.

Regards

I suggest you to follow : https://www.khanacademy.org/science/physics/mechanical-waves-and-sound/mechanical-waves/v/wave-equation

https://core.ac.uk/download/pdf/78533784.pdf

Article Algebraic travelling waves for the generalized Burgers-Fisher equation

https://www.sciencedirect.com/science/article/abs/pii/S0022247X18306188