Theoretical analysis reveals novel trigonometric background solutions for discrete and continuous Schwarzian Korteweg–de Vries equations, expanding analytical techniques for nonlinear systems.
In the paper we derive new solutions for the discrete and continuous Schwarzian Korteweg–de Vries (SKdV) equations. These solutions are characterized by trigonometric functions as backgrounds. For the discrete SKdV equation, its solutions are derived by using trigonometric function seeds and Bäcklund transformation. Solutions for the continuous SKdV equation are obtained by taking continuum limits.
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Wang et al. (2025) studied this question.
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