Numerical study investigates the stability of solitary waves in a nonlinear model, indicating critical conditions for instability.
We study the nonlinear Schrödinger equation with a competing cubic–quintic power‐law nonlinearity on the waveguide domain . This model is globally well‐posed and admits line solitary wave solutions, whose transverse (in‐)stability is numerically investigated. We consider both spatially localized perturbations and periodic deformations of the line solitary wave and numerically confirm that there exists a critical torus length above which instability appears.
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Klein et al. (2026) studied this question.
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