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- W4226181572 abstract "We study the problem of gravity surface waves for the ideal fluid model in the (2+1)-dimensional case. We apply a systematic procedure for deriving the Boussinesq equations for a prescribed relationship between the orders of four expansion parameters, the amplitude parameter $$alpha $$ , the long-wavelength parameter $$beta $$ , the transverse wavelength parameter $$gamma $$ , and the bottom variation parameter $$delta $$ . We also take into account surface tension effects when relevant. For all considered cases, the (2+1)-dimensional Boussinesq equations cannot be reduced to a single nonlinear wave equation for surface elevation function. On the other hand, they can be reduced to a single, highly nonlinear partial differential equation for an auxiliary function f(x, y, t) which determines the velocity potential but is not directly observed quantity. The solution f of this equation, if known, determines the surface elevation function. We also show that limiting the obtained the Boussinesq equations to (1+1)-dimensions one recovers well-known cases of the KdV, extended KdV, fifth-order KdV, and Gardner equations." @default.
- W4226181572 created "2022-05-05" @default.
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- W4226181572 date "2022-04-01" @default.
- W4226181572 modified "2023-10-18" @default.
- W4226181572 title "Boussinesq’s equations for (2+1)-dimensional surface gravity waves in an ideal fluid model" @default.
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- W4226181572 doi "https://doi.org/10.1007/s11071-022-07385-8" @default.
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