Exact Solution in Chaotic Inflation Model with Potential Minima

Taking the cosmological expansion rate directly as a function of field φ, H=H(φ), we present a new exact solution to Einstein's equations that describe the evolution of cosmological chaotic inflation model. The inflation is driven by the evolution of scalar field with inflation potential V(φ)=(λ/8)(φ²-υ²)². The spectral indices of the scalar density n_s and gravitational wave fluctuations n_g are computed. The value of n_s lies well inside the limits set by the cosmic background explorer satellite.     

An exact inflationary solution in the chaotic model with non-minimal coupling

This paper presents a new exact inflationary solution to the non-minimally coupled scalar field. The inflation is driven by the evolution of a scalar field with inflation potential V(φ ) = (λ/ 4)φ⁴+ b₁ φ²+ b₂ + b₃ φ^-2 + b₄ φ^-4. The spectral index of the scalar density fluctuations n_s is consistent with the result of WMAP3 (Wilkinson Microwave Anisotropy Probe 3) for λCDM (Lambda-Cold Dark Matter). This model relaxes the constraint to the quartic coupling constant. And it can enter smoothly into a radiation-dominated stage when inflation ends.     

Exact Solution for Jaynes-Cummings Model with Bosonic Field Nonlinearity and Strong Boson-Fermion Coupling

We use Lewis-Riesenfeld invariant approach to treat the modified Jaynes-Cummings models involving any forms of nonlinearty of the bosonic field when strong boson-fermion couplings are nilpotent Grassmann valued. The general state functions, time evolution operator and the time-evolution expressions for both the bosonic number and the fermionic number are presented.     

New Family of Exact Solutions and Chaotic Soltions of Generalized Breor-Kaup System in （2＋1）-Dimensions via an Extended Mapping Approach

Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized （2＋1）-dimensional Broer-Kaup system （GBK） system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the （2＋1）-dimensional GBK system.     

New Family of Exact Solutions and Chaotic Soltions of Generalized Breor-Kaup System in (2+1)-Dimensions via an Extended Mapping Approach

Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2 1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2 1)-dimensional GBK system.     

非球谐振子势的精确解

严格求解了三维非球谐振,势的Schrodinger方程给出了精确的能谱方程和归一化的径向波函数.获得了径向幂次算符r^s的矩阵元和平均值的计算公式及其递推关系.     

A Kind of Exact Inflationary Solution in the Chaotic Inflation Model to Non-minimally Coupled Scalar Field

We present a kind of exact inflationary solution in the chaotic inflation scenario to non-minimal coupled scalar field, taking the Hubble parameter directly as a function of the scalar field φ, H（φ） = αφ^n. Using the analysis of the WMAP3 data, we give the range of power index n.     

Some Exact Solutions of Variable Coefficient Cubic-Quintic Nonlinear Schrodinger Equation with an External Potential

By constructing appropriate transformations and an extended elliptic sub-equation approach, we find some exact solutions of variable coefficient cubic-quintie nonlinear Schrodinger equation with an external potential, which include bell and kink profile solitary wave solutions, singular solutions, triangular periodic wave solutions and so on.     

Chaotic Solutions of a Typical Nonlinear Oscillator in a Double Potential Trap

We have obtained a general unstable chaotic solution of a typical nonlinear oscillator in a double potential trap with weak periodic perturbations by using the direct perturbation method. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding chaotic region and orbits in parameter space are described by numerical simulations.     

An Exact Solution to the Two-Particle Boltzmann Equation System for Maxwell Gases

An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given.     

Exact Solution of a Many-Level Atom Interacting with a Monochromatic Field Without Rotating Wave Approximation

In the coherent-state representation, the technique applied to the Jaynes-Cummings (JC) model in the absence of rotating wave approximation (RWA) is extended to the treatment of a many-level atom interacting with a monochromatic field. Some general results are presented.     

A Model with Exact Inflationary Solution in Finsler Universe

In this paper, using the Gravity’s Rainbow theory, we introduce rainbow metric into rainbow Robertson-Walker metric, and obtain a model which depends on the energy of probe particles. Furthermore, we research on an exact inflationary solution of the model, and it can be consistent with the conclusions of observation. The results of our research show that some details in inflation depend on the energy of particles which are observed by observers.     

Allowed Parameter Regions for a Tree—Level Inflation Model

The early universe inflation is well known as a promising theory to explain the origin of large-scale structure of universe and to solve the early universe pressing problems.For a reasonable inflation model,the potential during inflation must be very flat,at least,in the direction of the inflaton.TO construct the inflaton potential all the known related astrophysics observations should be included.For a general tree-level hydrid inflation potential,which is not discussed fully so far,the parameters in it are shown how to be constrained via the astrophysics data observed and to be obtained to the expected accuracy,and to be consistent with cosmology requirements.     

Solution of Klein-Gordon Equation for Pseudo-Coulomb Potential Plus a New Ring-Shaped Potential

Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of the Klein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously, energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions are expressed by confluent hypergeogetric and hypergeogetric functions respectively.     

New Exact Solutions and Dynamics in （3＋1）-Dimensional Gross-Pitaevskii Equation with Repulsive Harmonic Potential

Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the （3＋1）-dimensional Gross-Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.     

Exact Solutions of Nonlinear Dynamics Equation in a New Double-Chain Model of DNA

The exact solutions of the general nonlinear dynamic system in a new double-chain model of DNA are studiedkink shape excitations can be found in both the Conte's truncation expansion and the Pickering's truncation expansion.Three types of new localized excitations, the asymmetric kink-kink excitations, the soliton-kink excitation, and thekink-soliton excitations, are found by using the Pickering's nonstandard truncation expansion.     

Integrable KP Coupling and Its Exact Solution

The integrable coupling is one of the most important topics in the nonlinear physics. This paper creates a novel integrable KP coupling and solves it via a recently-developed dark parameterization procedure.     

Exact Eigenfunctions of N-body System with Quadratic Pair Potential

We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave functions and the degree of degeneracy. By comparison, we refine Avinash Khare's results by making some items in his article precisely.     

Exact Eigenfunctions of N-body System with Quadratic Pair Potential

We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave functions and the degree of degeneracy. By comparison, we refine Avinash Khare's results by making some items in his article precisely.