Results 1 to 10 of about 23 (22)
Forum of Mathematics, Sigma, 2015 We introduce a novel solution concept, denoted ${\it\alpha}$-dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system on the line with ...
KATRIN GRUNERT +2 more
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Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 131-145, 1999., 1999 The Cauchy problem for the damped Boussinesq equation with small initial data is considered in two space dimensions. Existence and uniqueness of its classical solution is proved and the solution is constructed in the form of a series. The major term of its long‐time asymptotics is calculated explicitly and a uniform in space estimate of the residual ...
Vladimir V. Varlamov
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Analytical behavior of weakly dispersive surface and internal waves in the ocean
Journal of Ocean Engineering and Science, 2022 The (2+1)-dimensional interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis is described by the space-time fractional Calogero-Degasperis (CD) and fractional potential Kadomstev-Petviashvili (PKP) equation.
Mohammad Asif Arefin +3 more
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Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 643-648, 1999., 1999 The generalized forced Boussinesq equation, utt − uxx + [f(u)]xx + uxxxx = h0, and its periodic traveling wave solutions are considered. Using the transform z = x − ωt, the equation is converted to a nonlinear ordinary differential equation with periodic boundary conditions.
Kenneth L. Jones, Yunkai Chen
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Journal of Ocean Engineering and Science, 2022 This work aims to construct exact solutions for the space-time fractional (2 + 1)- dimensional dispersive longwave (DLW) equation and approximate long water wave equation (ALW) utilizing the two-variable (G′/G,1/G)-expansion method and the modified ...
Mohammad Asif Arefin +3 more
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Nearly conconcentric Korteweg‐de Vries equation and periodic traveling wave solution
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 183-187, 1998., 1998 The generalized nearly concentric Korteweg‐de Vries equation is considered. The author converts the equation into the power Kadomtsev‐Petviashvili equation . Solitary wave solutions and cnoidal wave solutions are obtained. The cnoidal wave solutions are shown to be representable as infinite sums of solitons by using Fourier series expansions and ...
Yunkai Chen
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Abstract and Applied Analysis, Volume 2, Issue 3-4, Page 281-299, 1997., 1997 For the damped Boussinesq equation , the second initial‐boundary value problem is considered with small initial data. Its classical solution is constructed in the form of a series in small parameter present in the initial conditions and the uniqueness of solutions is proved. The long‐time asymptotics is obtained in the explicit form and the question of
Vladimir V. Varlamov
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Conservation laws for incompressible fluids
International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 2, Page 377-384, 1989., 1989 By means of a direct approach, a complete set of conservation laws for incompressible fluids is determined. The problem is solved in the material (Lagrangian) description and the results are eventually rewritten in the spatial (Eulerian) formulation. A new infinite family of conservation laws is determined, besides those for linear momentum, angular ...
G. Caviglia, A. Morro
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Alexandria Engineering Journal, 2022 The space–time fractional coupled modified equal-width equation and the coupled Boussinesq equation are a category of fractional partial differential equations, which might be crucial mathematical feathers in nonlinear optics, solid-state physics ...
M. Ayesha Khatun +4 more
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On singularities of capillary surfaces in the absence of gravity
International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 1, Page 81-87, 1983., 1983 We study numerical solutions to the equation of capillary surfaces in trapezoidal domains in the absence of gravity when the boundary contact angle declines from 90° to some critical value. We also discuss a result on the behavior of solutions in more general domains that confirms numerical calculations.
V. Roytburd
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