Related papers: Whitham equations and phase shifts for the Kortewe…
Perturbative corrections to the mean field theory for particle-hole instabilities of interacting electron systems are computed within a scheme which is equivalent to the recently developed variational approach to the Kohn-Luttinger…
Solitons and cavitons (localized solutions with singularities) for the nonlocal Whitham equations are studied. The equation of a fourth order with a parameter in front of fourth derivative for traveling waves is reduced to a reversible…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent…
These short notes present to the reader (students, in particular) a concise approach to the derivation of the propagator of Hamiltonians with position-dependent kinetic energy. The formalism is applied to the von Roos Hamiltonian with…
The dipole-coupled two-level atoms(qubits) in a single-mode resonant cavity is studied by extended bosonic coherent states. The numerically exact solution is presented. For finite systems, the first-order quantum phase transitions occur at…
We perform enhanced Lie symmetry analysis of generalized fifth-order Korteweg-de Vries equations with time-dependent coefficients. The corresponding similarity reductions are classified and some exact solutions are constructed.
By Wertheim-method the exact solution of the Percus-Yevick integral equation for a system of particles with the repulsive step potential interacting (collapsing hard spheres) is obtained. On the basis of this solution the state equation for…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by…
It is shown that equations of the Korteweg-de Vries hierarchy and their conservation laws can be expressed via the whole powers of an integro-differential operator and functions provided by them.
Finite difference schemes that preserve two conservation laws of a given partial differential equation can be found directly by a recently-developed symbolic approach. Until now, this has been used only for equations with quadratic…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
In this article we consider the problem of unique continuation for a class of high order equations of Korteweg-de Vries type which include the kdV hierachy. It is proved that if the difference w of two solutions of an equation of this form…
In this paper, the Wheeler-DeWitt equation in full superspace formalism will be written in a matrix valued first-order formalism. We will also analyse the Wheeler-DeWitt equation in minisuperspace approximation using this matrix valued…
We study first-order electroweak phase transitions nonperturbatively, assuming any particles beyond the Standard Model are sufficiently heavy to be integrated out at the phase transition. Utilising high temperature dimensional reduction, we…
This paper proposes a new class of arbitrarily high-order conservative numerical schemes for the generalized Korteweg-de Vries (KdV) equation. This approach is based on the scalar auxiliary variable (SAV) method. The equation is…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
Numerical schemes that conserve invariants have demonstrated superior performance in various contexts, and several unified methods have been developed for constructing such schemes. However, the mathematical properties of these schemes…
A simplified Ginzburg-Landau theory is presented to study generally a coupling of a first-order phase transition (FOPT) to a second-order phase transition (SOPT). We show analytically that, due to the coupling between the two phase…