A General Korteweg-de Vries-Burgers Equation: Novel Ideas and Novel Results (Journal of Nonlinear Modeling and Analysis, 2025)
We consider the Cauchy problem for a general Korteweg-de Vries-Burgers equation and the Cauchy problem for the corresponding linear equation. We will couple together a few novel ideas, several existing ideas andexisting results and use rigorous mathematical analysis to accomplish severalvery important and very interesting results for these Cauchy problems.
Keywords: General Korteweg-de Vries-Burgers equation; global smooth solution; existence and uniqueness; sharp rate decay estimates; exact limits; optimal decay estimates.