[PDF] Top 20 Analytic solutions for Long’s equation and its generalization

... this equation drop out when β = 0. The approximate solutions that are de- rived from ...these solutions even under the assumption that the base flow is ...the solutions that are derived from ... See full document

... the analytic function spaces involving generalized derivative Γ , enabling us to get an additional regularity with respect to operator Γ , hence we obtain the ... See full document

... the analytic solution of Duffing type nonlinear integro- differential equation with integral boundary conditions is developed by applying the method of generalized ... See full document

... structures with N = ; Figure  exhibits the second-order RW interaction structures with N = ; Figure  exhibits the third-order RW interaction structures with N = . Solutions and figures obtained in this paper ... See full document

... parametric generalization short-cut derived from the NU have been used to carry out the analytic bound states (real energy spectrum and wave functions) of the KG equation with any orbital quantum ... See full document

... Ginocchio[] showed that there is a connection between pspin symmetry and near equalityof the time component of a vector potential and the scalar potential, ≈ − . After that, Meng et al [, ] derived that if Zg F ZF = 0 or ... See full document

... Boussinesq-Burgers equation is ...new solutions are given, including travelling wave solutions, periodic solutions and soliton and so ... See full document

... periodic solutions of the nonlinear ordinary differential equations that were introduced by Somioleko And the result of this study which is the using the periodic solutions on a wide range in difference ... See full document

... analytical solutions of the time-fractional Black-Scholes equation for European call option via a proposed relatively new semi-analytic technique hereby referred to as Projected Differential ... See full document

... (K-S) equation, which describes long nonlinear pressure waves in a liquid containing gas ...K-S equation. Secondly, using the symmetry groups, exact solutions which are invariant ... See full document

... The rest of this paper is organized as follows: In Section II, the vector fields of Eq. (1) are presented by using Lie symmetry analysis method. Based on the optimal dynamical system method, all the similarity reductions ... See full document

... measure solutions to the conservative renewal equation and analyze their long time ...The solutions are built by using a duality ...the solutions to the ... See full document

... [2] Kosuke Ono. On global existence, asymptotic stability and blowing up of solutions for some degenerate non-linear wave equations of Kirchhoff type with strong dissipation [J]. Mathematical Methods in the ... See full document

... equations arises in quantum mechanics. It describes how the quantum state of some physical system changes with time. We show that the system under consideration admits a global solution in appropriate functional spaces. ... See full document

... The solutions of these nonlinear systems are dominated by their singularities: physically, a real singularity controls the local behaviour of a ...a long tradition in applied mathematics to solve nonlinear ... See full document

... < s <1. However, the function Γ(s)Ψ ν (s; 0) is not even defined in the cri- tical strip as the integral representation ...use analytic continuation [[6], ... See full document

... In this paper, we applied the homotopy analysis method (HAM) to solve the modified Kawahara equation. Numerical results demonstrate that the methods provide efficient approaches to solving the modified Kawahara ... See full document

... obtained analytic solutions, we have discussed the one- and two-solitary internal wave propagation and ...the analytic results obtained in this paper is helpful for further study on the deep ocean ... See full document

... in solutions that are even or odd, and have period π or semi-period π ...above equation with one of the above conditions constitutes a regular Sturm-Liouville eigenvalue ... See full document

... not only to state conditions for the existence and uniqueness of physically relevant solutions, but also to determine the asymptotic behaviour of solutions. For this we require the semigroup associated with ... See full document