Related papers: Nonsensitive nonlinear homotopy approach
The Homotopy Analysis Method (HAM) is a widely used analytical approach for solving nonlinear problems, yet its theoretical foundation lacks rigorous justification, and its intrinsic correlation with perturbation theory remains ambiguous,…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation…
In this paper we discuss a recent application of a variational homotopy perturbation method to rather simple nonlinear oscillators . We show that the main equations are inconsistent and for that reason the results may be of scarce utility.
A new non-perturbative approach is proposed to solve time-independent Schr\"{o}dinger equations in quantum mechanics and chromodynamics (QCD). It is based on the homotopy analysis method (HAM), which was developed by the author for highly…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
The analysis of nonlinear spectroscopy, widely used to study the dynamics and structures of condensed-phase matter, typically employs a perturbative approach noticing the weak interaction between the laser and the matter of interest.…
We consider adaptive control problem in presence of nonlinear parametrization of uncertainties in the model. It is shown that despite traditional approaches require for domination in the control loop during adaptation, it is not often…
In this study, a thorough investigation was conducted into the Homotopy Perturbation Method (HPM) and its application to solve the Burger and Blasius equations. The HPM is a mathematical technique that combines aspects of homotopy and…
This paper presents a new systematic framework for nonlinear singularly perturbed systems in which state-dependent perturbation functions are used instead of constant perturbation coefficients. Under this framework, general results are…
Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal…
Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian…
This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of {\em…
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are…
In this article, we apply Homotopy Perturbation Method (HPM) for solving three coupled non-linear equations which play an important role in biosystems. To illustrate the capability and reliability of this method. Numerical example is given…