On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations

The Laplace transformation is a very important integral transform,and it is extensively used in solving ordinary differential equations,partial differential equations,and several types of integro-differential equations.Our purpose in this study is to introduce the notion of fuzzy double Laplace transform,fuzzy conformable double Laplace transform(FCDLT).We discuss some basic properties of FCDLT.We obtain the solutions of fuzzy partial differential equations(both one-dimensional and two-dimensional cases)through the double Laplace approach.We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations.

Various Types of Kink and Bright Resonant Soliton Solutions for the (2+1)-Dimensional Double sine-Gordon Equation

The algebraic mapping relations between the(2+1)-dimensional double sine-Gordon equation and the cubic nonlinear Klein–Gordon equation are constructed. Many new types of two-dimensional resonant kink, bright soliton and solitoff solutions are obtained, such as broken line shape, "V" shape, "snake" shape and "M" shape solitary waves,Zigzag-curve type, "ω" shape, peroidic-curve type, oscillatory Arch-type and parabolic shape bright soliton waves. We also investigate the propagating properties of some soliton solutions.

Some New Exact Traveling Wave Solutions of Double-sine-Gordon Equation

double-sine-Gordon 方程借助于所谓的印射方法被学习。一些新准确答案是坚定的。

Separation Transformation and New Exact Solutions of the (N+1)-dimensional Dispersive Double sine-Gordon Equation

In this paper,the separation transformation approach is extended to the(N + 1)-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of 3 He superfluid.This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation.Then the general solutions of the set of partial differential equations are obtained and the nonlinear ordinary differential equation is solved by F-expansion method.Finally,many new exact solutions of the(N + 1)-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation.For the case of N > 2,there is an arbitrary function in the exact solutions,which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.

Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

A simple approach to solving double sinh–Gordon equation

By introducing an auxiliary ordinary differential equation and solving it by the method of variable separation abundant types of explicit and exact solutions for the double sinh-Gordon equation are derived in a simple manner.

SOLVING COUPLED PSEUDO-PARABOLIC EQUATION USING A MODIFIED DOUBLE LAPLACE DECOMPOSITION METHOD

In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems.

PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION

In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equationutt - uxx - auxxtt ＋ bux4 - duxxt = f（u）xxare proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.

Double Elzaki Transform Decomposition Method for Solving Non-Linear Partial Differential Equations

In this paper, we discuss a new method employed to tackle non-linear partial differential equations, namely Double Elzaki Transform Decomposition Method (DETDM). This method is a combination of the Double ELzaki Transform and Adomian Decomposition Method. This technique is hereafter provided and supported with necessary illustrations, together with some attached examples. The results reveal that the new method is very efficient, simple and can be applied to other non-linear problems.

Double Elliptic Equation Expansion Approach and Novel Solutions of (2+1)-Dimensional Break Soliton Equation

在这篇论文，借助于两倍椭圆形的方程扩大途径，新奇双非线性的波浪答案(2+1 ) 维的裂缝 soliton 方程被获得。这些双非线性的波浪答案包含双 Jacobi 椭圆形的像功能的答案，双独居的像波浪的答案等等。方法对一些另外的非线性的波浪方程在也强大(2+1 ) 尺寸。

Kinetic equations characterizing double reversible transformations in heating CuZnAlMnNi shape memory alloy

The apparent activation energies and frequency factors of thedouble reversible transformations occurring in heating CuZnAlMnNIshape memory alloy (SMA) were deduced as ΔE_x→M = 62. 597 8 KJ/mol, ΔE_M → A = 153. 92 KJ/Mol, A_x→M = 5.2232 × 10~9S^-1, andA_ M → A = 2.3251 × 10~23 S^-1, respectively. The kinetic equationsof the two transformations due- Ing heating were establishedsimultaneously.

Exact solutions of the Dirac equation with Pschl-Teller double-ring-shaped Coulomb potential via the Nikiforov-Uvarov method

Exact analytical solutions of the Dirac equation are reported for the Poschl-Teller double-ring-shaped Coulomb potential.The radial,polar,and azimuthal parts of the Dirac equation are solved using the Nikiforov-Uvarov method,and the exact bound-state energy eigenvalues and corresponding two-component spinor wavefunctions are reported.

BIFURCATION OF SINGULAR POINTS NEAR A DOUBLE FOLD POINT INZ_2 -SYMMETRIC NONLINEAR EQUATIONS

We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.

Shot noise in electron transport through a double quantum dot:a master equation approach

We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dynamics. The approach based on the occupation-state basis, despite being widely used in many previous studies, is valid only when the interdot coupling strength is much smaller than the energy difference between the two dots. In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling. Using realistic model parameters, we demonstrate that the predicted currents and shot-noise properties from the two approaches are significantly different when the interdot coupling is not small. Furthermore, properties of the shot noise predicted using the eigenstate basis successfully reproduce qualitative features found in a recent experiment.

Lie Symmetry Reductions and Exact Solutions of a Multidimensional Double Dispersion Equation

In this paper, based on classical Lie group method, we study a multidimensional double dispersion equation, and get its infinitesimal generator, symmetry group and similarity reductions. In particular, similarity solutions and travelling wave solutions of the multidimensional double dispersion equation are derived from the reduction equations.

An Analysis of Double Laplace Equations on a Concave Domain

In the investigation, the complex geometric domain is a concave geometrical pattern. Due to the symmetric character, the left side of the geometric pattern,?i.e.?the L-shaped region is calculated in the study. The governing equation is expressed with?Laplace?equations. And the analysis is solved by eigenfunction expansion and point-match method. Besides, visual?C++?helps obtain the results of numerical calculation. The local values and the mean values of the function are also discussed in this study.

Double Elzaki Transform Decomposition Method for Solving Third Order Korteweg-De-Vries Equations

In this study, we used Double Elzaki Transform (DET) coupled with Adomian polynomial to produce a new method to solve Third Order Korteweg-De Vries Equations (KdV) equations. We will provide the necessary explanation for this method with addition some examples to demonstrate the effectiveness of this method.

Hidden Properties of Mathematical Physics Equations. Double Solutions. The Realization of Integrable Structures. Emergence of Physical Structures and Observable Formations

With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.

Reconstructing Equation of State for Dark Energy in Double Complex Symmetric Gravitational Theory

<正> We propose to study the accelerating expansion of the universe in the double complex symmetric grav-itational theory(DCSGT).The universe we live in is taken as the real part of the whole spacetime M_C~4(J),which isdouble complex.By introducing the spatially fiat FRW metric,not only the double Friedmann equations but also thetwo constraint conditions p_J=0 and J~2=1 are obtained.Fhrthermore,using parametric D_L(z)ansatz,we reconstructthe ω'(z)and V(φ)for dark energy from real observational data.We find that in the two cases of J=i,pJ=0,andJ=ε,pJ≠0,the corresponding equations of state ω'(z)remain close to-1 at present(z=0)and change from below-1 to above -1.The results illustrate that the whole spacetime,i.e.the double complex spacetime M_C~4(J),may beeither ordinary complex(J=i,p_J=0)or hyperbolic complex(J=e,p_J≠0).And the fate of the universe would beBig Rip in the future.

Double Wronskian Solutions of Non-Isospectral Levi Equations

The double Wronskian solutions of the non-isospectral Levi equations are derived through Wronskian technique.