Global solvability of initial boundary-value problems for nonlinear analogs of the Boussinesq equation

Amirov, Sh. Sh.; Кожанов, А. И.

doi:10.1134/s0001434616010211

Cited by 3 publications

(4 citation statements)

References 2 publications

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“…Here, q(ξ ) is a continuous function. For such an equation, the solvability of different boundary-value problems has been proven by imposing certain conditions into the function q(ξ ) [1]. As a continuation of this study, the boundary-value problem was solved to find approximate solutions and the stability of the solution under certain conditions were investigated [2].…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions for the Boussinesq equation with nonlinearity in the time-derivative term using polynomial function methods

Amirov¹,

Bostanci²

2019

ntmsci

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In this study, solitary wave solutions were obtained by using polynomial function method for some cases in the 6th order nonlinear modified Boussinesq equation. The difference of this study from the other studies in the literature is that the Boussinesq equation and its analogues, which had been studied so far, had non-linearity in the terms having derivatives with respect to the space variables. However, in this study, the non-linearity is found in the time-derivative terms of the analogues of the Boussinesq equation.

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Section: Introductionmentioning

confidence: 99%

Soliton solutions for the Boussinesq equation with nonlinearity in the time-derivative term using polynomial function methods

Amirov¹,

Bostanci²

2019

ntmsci

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“…Although the specification of the Hamiltonian is beyond the scope of this paper, this assumption is physically reasonable since the initial boundary value problem for Eq. (7) has a unique solution [22]. Then, the solution u(t, x) of Eq.…”

Section: Physical Interpretation Of the Problemmentioning

confidence: 99%

“…, there exists at least one solution, in the space V , for the initial boundary value problem (1), (2), (3) [22]. q(ξ ) and the functions u 0 (x), u 1 (x), f (t, x) must be chosen in accordance with Theorem 1 and Theorem 2.…”

Section: Theorem 2 If the Function Q(ξ ) Satisfies Both The Conditiomentioning

confidence: 99%

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Boundary value problem for the nonlinear analogues of the Boussinesq equation: Numerical solution and its stability

Anutgan¹,

Amirov²

2017

ntmsci

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Abstract:The recent work on the solvability of the boundary value problem for the nonlinear analogue of the Boussinesq equation has been further extended to focus on the characteristics of the solution. Since this type of equation does not have a known analytical solution for arbitrary boundary conditions, the problem has been solved numerically. The stability of the solution and the effect of the input function on the stability have been investigated from the physics point of view. For the special case of a discontinuous function at the right hand side of the equation, the solution has been analyzed around the discontinuity points.

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Analytical Solitary Wave Solutions for the Nonlinear Analogues of the Boussinesq and Sixth-Order Modified Boussinesq Equations

Amirov¹,

Anutgan²

2017

jaac

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Global solvability of initial boundary-value problems for nonlinear analogs of the Boussinesq equation

Cited by 3 publications

References 2 publications

Soliton solutions for the Boussinesq equation with nonlinearity in the time-derivative term using polynomial function methods

Soliton solutions for the Boussinesq equation with nonlinearity in the time-derivative term using polynomial function methods

Boundary value problem for the nonlinear analogues of the Boussinesq equation: Numerical solution and its stability

Analytical Solitary Wave Solutions for the Nonlinear Analogues of the Boussinesq and Sixth-Order Modified Boussinesq Equations

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