Partially integrable generalizations of classical integrable models by combination of characteristics method and Hopf-Cole transformation

2012/10/26 by A. I. Zenchuk, Zenchuk, A. I.
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1210.7089

openalex publication_date 2012/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We represent an integration algorithm combining the characteristics method and Hopf-Cole transformation. This algorithm allows one to partially integrate a large class of multidimensional systems of nonlinear Partial Differential Equations (PDEs). A specific generalization of the equation describing the dynamics of two-dimensional viscous fluid and a generalization of the Korteweg-de Vries equation are examples of such systems. The richness of available solution space for derived nonlinear PDEs is discussed.

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