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- W4308491172 abstract "Abstract This paper investigates the problem of the orbital stability of dn periodic wave solutions of the Boussinesq equation with quadratic-cubic nonlinear terms. First, the dn periodic wave solution of the studied equation is solved by using the integral method and the knowledge of elliptic functions, and the existence of smooth curves of dn periodic wave solutions with fixed period L is proved. Then the Floquet theory and Wely’s essential spectrum theorem are applied to the spectral analysis of the operator, and obtain its spectral properties. Finally, according to the ideas for proving the stability of solitary wave solutions from Benjamin and Bona et al., by overcoming the complexity caused by the quadratic-cubic nonlinear terms in the studied equation, we prove the dn periodic wave solution of the studied equation is orbitally stable under small perturbations of the $$L^{2}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> norm." @default.
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- W4308491172 date "2022-11-03" @default.
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- W4308491172 title "Orbital Stability of dn Periodic Wave Solutions of the Boussinesq Equation with Quadratic-Cubic Nonlinear Terms" @default.
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- W4308491172 doi "https://doi.org/10.1007/s44198-022-00091-4" @default.
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