Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

First Year – Fall ......................... .............................................................................................. Credits MAT 210 ..................................... Calculus I ............................................................................. 4.0 ENG 110...................................... Expository Writing ............................................................. 3.0 CHE 210 ...................................... Chemistry I .......................................................................... 4.0 HUM 100 OR SOC 101 OR PSY 101 ........................................................................................ 6.0 Subtotal ...................................... .............................................................................................. 17

Chemical Engineering Scienceについて

The english translation

For the exponential traveling wave solutions to the Hirota bilinear equations, a sufficient and necessary criterion for the existence of linear superposition principle has been given. Motivated by this criterion, we propose a new Hirota bilinear equation via using a multivariate polynomial. Applying the linear superposition principle to this new Hirota bilinear equation, we finally find two types of resonant multiple wave solutions, among which, the resonant three-wave solutions are illustrated with three-dimensional plots.

Resonant behavior of multiple wave solutions to a Hirota bilinear equation

We construct new analytical solutions of the ( 3 + 1 )-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

/pdf/new-traveling-wave-solutions-of-the-higher-dimensional-1qlmqxn8b3.pdf

New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

• The nonlinear Schrödinger’s equation with anti-cubic nonlinearity is considered. • The Kundu-Mukherjee-Naskar model is considered. • The analytical solutions are obtained via Bernoulli approximation method and Hermite approximation method. Optical fibers have a major role in the industry and daily life. To simulate the pulse propagation in optical fibers, numerous models are seen in the literature. In this work, the Kundu-Mukherjee-Naskar (KMN) model and the anti-cubic Schrödinger equation are considered. To solve these models, ansatz-based methods are considered and also, the problem about the determination of transformation is replied so that it is not clear in the literature. The results of the proposed models will play a key role in applications in nonlinear optics, fluid dynamics, quantum mechanics and various other branches of science. 

The soliton analysis for optical fibers models

Rogue waves and solitons of the generalized modified nonlinear Schrödinger equations

https://lirias.kuleuven.be/bitstream/123456789/456754/1/Homotopy_ACOMEN.pdf

Understanding Population Balances Involving Aggregation and Breakage Through Homotopy Approaches

To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas type equations. The proposed Fibonnacci&Lucas approximation method produces many new solutions. Consequently, we introduce new exact travelling wave solutions of some physical systems in terms of these new solutions of the Fibonacci&Lucas type equation. In addition to using different ansatz, we use determine different balancing principle to obtain optimal solutions.

The Solutions of Nonlinear Heat Conduction Equation via Fibonacci&Lucas Approximation Method

/pdf/a-note-for-finding-exact-solutions-of-some-nonlinear-57t8q3l9eo.pdf

Zehra Pinar

Papers

The soliton analysis for optical fibers models

Rogue waves and solitons of the generalized modified nonlinear Schrödinger equations

Understanding Population Balances Involving Aggregation and Breakage Through Homotopy Approaches

The Solutions of Nonlinear Heat Conduction Equation via Fibonacci&Lucas Approximation Method

A note for finding exact solutions of some nonlinear differential equations