Nonlinear Effects and Run-up of Coastal Waves Generated by Billiards with Semi-rigid Walls in the Framework of Shallow Water Theory

Author:

Dobrokhotov S. Yu.,Nazaikinskii V. E.,Tsvetkova A. V.

Publisher

Pleiades Publishing Ltd

Subject

Mathematics (miscellaneous)

Reference21 articles.

1. A. Yu. Anikin, S. Yu. Dobrokhotov, and V. E. Nazaikinskii, “Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem,” Math. Notes 104 (3–4), 471–488 (2018) [transl. from Mat. Zametki 104 (4), 483–504 (2018)].

2. A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, and A. V. Tsvetkova, “Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems,” Theor. Math. Phys. 201 (3), 1742–1770 (2019) [transl. from Teor. Mat. Fiz. 201 (3), 382–414 (2019)].

3. A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, and A. V. Tsvetkova, “Asymptotics, related to billiards with semi-rigid walls, of eigenfunctions of the $$\nabla D(x)\nabla $$ operator in dimension $$2$$ and trapped coastal waves,” Math. Notes 105 (5–6), 789–794 (2019) [transl. from Mat. Zametki 105 (5), 792–797 (2019)].

4. A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, and A. V. Tsvetkova, “Asymptotic eigenfunctions of the operator $$\nabla D(x)\nabla $$ defined in a two-dimensional domain and degenerating on its boundary and billiards with semi-rigid walls,” Diff. Eqns. 55 (5), 644–657 (2019) [transl. from Diff. Uravn. 55 (5), 660–672 (2019)].

5. A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, and A. V. Tsvetkova, “Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for 2D standing coastal waves,” St. Petersbg. Math. J. 33 (2), 185–205 (2022) [transl. from Algebra Analiz 33 (2), 5–34 (2021)].

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1. Asymptotics of Long Nonlinear Coastal Waves in Basins with Gentle Shores;Russian Journal of Mathematical Physics;2024-03

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