In the manuscript under investigation, the dual-mode form of nonlinear Schr ödinger equation was examined. This model is used for studying the enlargement or absorption of dual waves in the ...occurrence of nonlinearity and distribution effects. Bright, dark, combined bright-dark, singular soliton, periodic, rational and solitary wave solutions of this equation are obtained. Preferred integration schemes are the extended
(
G
′
/
G
)
, sine-cosine, and semi-inverse methods. Numerical simulations of the obtained solutions were carried out for the special values of the parameters in the solutions and 3D and contour graphs were drawn. The convergence analysis of the performed schemas to the model were also demonstrated.
We consider periodic solutions of the following problem associated with the fractional Laplacian:
in
. The smooth function
is periodic about
and is a double-well potential with respect to
with wells ...at
and -1 for any
. We prove the existence of periodic solutions whose periods are large integer multiples of the period of
about the variable
by using variational methods. An estimate of the energy functional, Hamiltonian identity and Modica-type inequality for periodic solutions are also established.
The effects of the heterogeneity of liquid on the tank sloshing under pitching excitation are analyzed and discussed. The time history of the free surface elevation for tank containing a homogeneous ...– heterogeneous liquid are recorded and discussed. Numerical simulations are performed for various functions of density using the finite-element method. A theoretical model in the case of heterogeneous viscous liquid are developed using the variation formulation based on the Navier-Stokes equations. The effect of viscosity on the responses is also discussed for each case. In each case, the time history plots for the vertical fluid displacement at a select node, and the pressure in selected elements are presented to illustrate the results of numerical simulations. The effect of heterogeneity parameter of the amplitude of liquid sloshing in a two dimensional partially filled rectangular tank under pitch excitation is conducted to investigate the effects of excitation variable density on the liquid sloshing by a series of numerical experiments. The results are compared with existing theoretical study and the comparison shows fair agreement.
In this article, we focus on triple weak solutions for nonlinear elliptic problems with Dirichlet boundary condition. We show the existence of at least three distinct weak solutions by using ...variational methods and a recent obtained three critical points theorem under suitable assumptions.
The propagation of electromagnetic waves in the plasma sheath is investigated theoretically and numerically using the variational method, which handles the inhomogeneity of the plasma sheath. We ...derive the variation of the action integral, which can be numerically represented by expanding the velocity and electromagnetic fields to the piecewise polynomial function space. We analyze the transmissivity of electromagnetic waves propagating through the plasma sheath with the barrier and the barrier-parabolic electron number density profile. We give the frequency-dependent transmissivity of electromagnetic wave propagation in different inhomogeneous plasma sheaths. The electromagnetic energy density derived from the Lagrangian density is also given, and the result shows that the collision between electrons and neutral particles can be used to enhance the transmission of electromagnetic waves in the plasma sheath.
•Second-order differential form of even-parity SPN equations are derived.•New interface and boundary conditions are derived unlike traditional SPN.•Equivalence with GSPN for K = 0 is brought out.
...Simplified PN (SPN) equations are derived based on variational method using a modified version of ansatz originally proposed by Pomraning. New boundary and interface conditions are derived for the SPN equations using the corresponding angular flux expression. The equivalence of equations, thus derived, along with its interface and boundary conditions with those of a specific case of Generalized SPN (GSPN), put forward by Chao, is brought out.
We consider the problem of bending of a three-layer shallow shell resting on an elastic foundation under the action of a transverse load. It is assumed that the lower and upper layers are made of ...functionally graded materials and the filler is made of an isotropic material (metal or ceramic). For the mathematical modeling of the problem, we use the refined first-order Timoshenko-type theory of plates that takes into account the presence of bending strains. The elastic foundation of the shell is modeled by a Pasternaktype two-parameter model. The effective elastic properties of the functionally graded materials vary according to the power law. The proposed algorithm for solving the problems of bending is based on the application of the
R
-functions theory and the Ritz variational method. The developed software, which realizes the proposed approach, is verified by analyzing test problems posed for rectangular plates and shallow shells with different schemes of arrangement of the layers and various characteristics of the elastic foundation. The efficiency of the method is demonstrated by an example of a shell with hexagonal hole and circular notches on the sides. We consider various conditions of fastening of the hole and the outer contour of the shell. The influence of the gradient index and the characteristics of elastic foundation on the maximum value of deflection are analyzed. The obtained results are presented in the form of tables and plots. They are used to study functionally graded plates and shallow shells on an elastic foundation with complex shape in the plan.
This paper shows the existence of solutions for problem involving the p(x)-Laplacian in RN with an indefinite weights a and b, by means of the Sobolev embedding theorem and under some various ...conditions on the nonlinearity.
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