The Lie group theoretic approach is employed here to obtain inequivalent invariant solutions of a system nonlinear partial differential equations (SNLPDEs) in (1+1)-dimensions appearing the mathematical analysis shallow water waves finite amplitude, tsunami particular. It found that admits five-parameter symmetry transformations with algebra \(\mathcal{G}\) infinitesimal generators. An optimal set \(\mathcal{OG}_1\) eighteen one-dimensional subalgebras has been obtained. Similarity variables...

An approximation scheme based on orthonormal Legendre polynomial wavelets has been proposed here to obtain the approximate solution of Fredholm integral equations second kind with a logarithmic singular kernel. In conjunction double exponential quadrature, Galerkin approach is exercised convert equation system linear algebraic unknown coefficients elements wavelet basis. estimate posteriori error in provided. exercise for some test examples exhibits that method (i) efficient, (ii) rapidly...

It is observed that the well-known shifted large-N technique proposed by Imbo, Pagnamenta, and Sukhatme [Phys. Rev. D 29, 1669 (1984)] fails to yield correct behavior of bound-state wave function for Morse oscillator. To remove this inadequacy, we propose a modified approach which not only restores exact analytic expressions energy eigenvalues eigenfunctions oscillator but also predicts quite accurate results rotating

The shifted large-N expansion method, which was developed to obtain accurate energy eigenvalues for nonrelativistic-potential problems, has been extended deal with a relativistic particle (with or without spin) bound in spherically symmetric potential. calculations are carried out any arbitrary quantum state using terms of parameter 1/k\ifmmode\bar\else\textasciimacron\fi{}, where k\ifmmode\bar\else\textasciimacron\fi{} contains the dimension space N and so-called shift parameter. Similar...

In this work, authors propose some modifications Adomian decomposition method to get accurate closed form approximate or exact solutions of Duffing- and Li´enard-type nonlinear ordinary differential equations.Results obtained by the revised scheme have been exploited subsequently derive constraints among parameters be bounded. The present appears efficient may regarded as confluence apparently different methods for getting a variety equations appearing mathematical models in several physical...

In this work, the rapidly convergent approximation method (RCAM) followed by appropriate modifications is applied to obtain piecewise smooth solutions and conserved quantities of a Liénard‐type equation some important nonlinear partial differential equations reducible former one. Explicit parameter dependence solution has been sensibly used determine constant motion as well domain in space for which bounded. Solution then find traveling wave corresponding Schrödinger equation. These findings...

The difficulties associated with application of the shifted large-N technique to Dirac equation have been resolved by applying method Klein-Gordon in which a spin-orbit interaction term is included analogous Pauli theory. Explicit analytical expressions for relativistic screened Coulomb bound-state energies, radial wave functions, and normalizations are given. For point-Coulomb problem, we restore exact results binding energies almost functions. 1/N expansion then compared numerical...

This work deals with analytical investigation of local qualitative temporal behavior around inner equilibrium point a model for three species food chain, studied earlier by Hastings and Powel others. As an initial step towards the spectral analysis model, governing equations have been split into linear nonlinear parts arbitrary point. The explicit parameter dependence eigenvalues Jacobi matrix associated to part derived. Analyzing these expressions in conjunction some pedagogical analysis,...

Abstract This paper is concerned with obtaining approximate numerical solution of a classical integral equation some special type arising in the problem cruciform crack. has been solved earlier by various methods literature. Here, approximation terms Daubechies scale function employed. The results for stress intensity factor obtained this method specific forcing term are compared to those available literature, and present appears be quite accurate.

Non-minimally coupled scalar field cosmology has been studied in this work within the framework of Einstein gravity. In background homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime non-minimally having self-interacting potential is taken as source matter content. The constraint imposing Noether symmetry on Lagrangian system not only determines infinitesimal generator (the vector) but also coupling function for field. By choosing appropriately a point...

The Dalgarno - Lewis summation technique as used in the Rayleigh Schrödinger perturbation theory is examined. It shown that this forms an independent and can be to deal with both bound- continuum-state problems some added advantage over other such approaches.