New soliton wave solutions of a(2+1)-dimensional Sawada-Kotera equation

In this work,we studied a(2+1)-dimensional Sawada-Kotera equation(SKE).This model depicts non-linear wave processes in shallow water,fluid dynamics,ion-acoustic waves in plasmas and other phe-nomena.A couple of well-established techniques,the Bäcklund transformation based on the modified Kudryashov method,and the Sardar-sub equation method are applied to obtain the soliton wave solution to the(2+1)-dimensional structure.To illustrate the behavior of the nonlinear model in an appealing fashion,a variety of travelling wave solutions are formed,such as contour,2D,and 3D plots.The pro-posed approaches are proved more convenient and dominant for getting analytical solutions and can also be implemented to a variety of physical models representing nonlinear wave phenomena.

Dispersive propagation of optical solitions and solitary wave solutions of Kundu-Eckhaus dynamical equation via modified mathematical method

In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general coefficients.In our knowledge earlier reported results of the KE equation with specific coefficients.These obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other branches.All calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences.

Traveling wave solutions of the nonlinear Gilson-Pickering equation in crystal lattice theory

This paper focuses on obtaining the traveling wave solutions of the nonlinear Gilson-Pickering equa-tion(GPE),which describes the prorogation of waves in crystal lattice theory and plasma physics.The solution of the GPE is approximated via the finite difference technique and the localized meshless radial basis function generated finite difference.The association of the technique results in a meshless approach that does not require linearizing the nonlinear terms.At the first step,the PDE is converted to a system of nonlinear ODEs with the help of the radial kernels.In the second step,a high-order ODE solver is adopted to discretize the nonlinear ODE system.The global collocation techniques pose a considerable computationl burden due to the calculation of the dense algebraic system.The proposed method approx-imates differential operators over the local support domain,leading to sparse differentiation matrices and decreasing the computational burden.Numerical results and comparisons are provided to confirm the efficiency and accuracy of the method.

Nonlocal symmetry and exact solutions of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation

In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the（2＋1）-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system.In addition,the（2＋1）-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion（CRE） solvable.As a result,the soliton–cnoidal wave interaction solutions of the equation are explicitly given,which are difficult to find by other traditional methods.Moreover figures are given out to show the properties of the explicit analytic interaction solutions.

Soliton solutions,travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics

Many physical systems can be successfully modelled using equations that admit the soliton solutions.In addition,equations with soliton solutions have a significant mathematical structure.In this paper,we study and analyze a three-dimensional soliton equation,which has applications in plasma physics and other nonlinear sciences such as fluid mechanics,atomic physics,biophysics,nonlinear optics,classical and quantum fields theories.Indeed,solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour.We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time.Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function,elliptic functions,elementary trigonometric and hyperbolic functions solutions of the equation.Besides,various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique.These solutions comprise dark soliton,doubly-periodic soliton,trigonometric soliton,explosive/blowup and singular solitons.We further exhibit the dynamics of the solutions with pictorial representations and discuss them.In conclusion,we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula.We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.

Solitons on a Periodic Wave Background of the Modified KdV-Sine-Gordon Equation

The Backlund transformation（BT） of the m Kd V-s G equation is constructed by introducing a new transformation. Infinitely many nonlocal symmetries are obtained in terms of its BT. The soliton-periodic wave interaction solutions are explicitly derived by the classical Lie-group reduction method. Particularly, some special concrete soliton and periodic wave interaction solutions and their behaviours are discussed both in analytical and graphical ways.