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Soliton propagation for a coupled schrödinger equation describing Rossby waves

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Chinese Physics B 2023年第7期32卷 206-215页

作者：徐丽阳尹晓军曹娜白淑婷 College of Science Inner Mongolia Agriculture UniversityHohhot 010018China

We study a coupled schrödinger equation which is started from the Boussinesq equation of atmospheric gravity waves by using multiscale analysis and reduced perturbation *** the coupled schrödinger equation,we obtain the Manakov model of all-focusing,all-defocusing and mixed types by setting parameters value and apply the Hirota bilinear approach to provide the two-soliton and three-soliton ***,we find that the all-defocusing type Manakov model admits bright-bright soliton ***,we find that the all-defocusing type Manakov model admits bright-bright-bright soliton ***,we go over how the free parameters affect the Manakov model’s allfocusing type’s two-soliton and three-soliton solutions’collision locations,propagation directions,and wave *** findings are useful for setting a simulation scene in Rossby waves *** answers we have found are helpful for studying physical properties of the equation in Rossby waves.

关键词： Hirota bilinear method schrödinger equation soliton solution Rossby waves

Life Is Quantum Biology Effects Explained from the schrödinger equation, Serious or Life-Threatening Conditions or Diseases, and COVID-19 Results

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Journal of Biosciences and Medicines 2022年第10期10卷 164-172页

作者： Huu S. Tieu Martin F. Loeffler Golden Sunrise Nutraceutical Inc. Porterville USA

Background: A plant based approach was undertaken to ascertain the efficacy of the Technology/Innovation of a new medical Technology based on similar activity to the circulatory system of plants. Basic Technology formulations were introduced into plant structures to evaluate the responses for cell division and plant growth which ultimately lead to the final product. This Technology/Innovation transforms and enhances common botanical/herb products such that they can be used to treat COVID-19 infection and Serious or Life-threatening conditions or diseases. They can restore the diseased cell’s abnormal metabolism to homeostasis and return it to normal function by slowing or reversing the cell’s malfunctioning metabolism, or in other words, slowing or reversing the disease process. Methods: A systematic treatment for COVID-19 infection and Serious or Life-threatening illness in patients is based on theories of traditional Chinese medicine. The Technology/Innovation is developed as dietary supplement products for treatment of Serious or Life-threatening conditions or diseases. Results: The results consist of over one hundred Serious or Life-threatening patient medical records. The U.S. Food and Drug Administration (FDA) reviewed/evaluated/accepted the Technology/Innovation patient medical record results, which included fifty-four COVID-19 patients with Prioritized Review Expedited No.: 2020-2867 CR2020-2596 information on September 16, 2020 and twenty-seven cancer patients Cancer Survival Rate Results in (Table 1) with FDA Establishment Identification No.: 3012327979 information on March 25, 2019 as FDA-Regulated medical products and meet the requirement under FDA Significant Scientific Agreement standards.

关键词： Cellular Therapy COVID-19 Serious or Life-Threatening Conditions or Diseases schrödinger equation Blood-Brain Barrier Immunology

An Optimized Perfectly Matched Layer for the schrödinger equation

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Communications in Computational Physics 2011年第1期9卷 147-179页

作者： Anna Nissen Gunilla Kreiss Department of Information Technology Uppsala UniversityP.O.Box 337SE-75105 UppsalaSweden.

We derive a perfectly matched layer(PML)for the schrödinger equation using a modal *** derive approximate error formulas for the modeling error from the outer boundary of the PML and the error from the discretization in the layer and show how to choose layer parameters so that these errors are matched and optimal performance of the PML is *** computations in 1D and 2D demonstrate that the optimized PML works efficiently at a prescribed accuracy for the zero potential case,with a layer of width less than a third of the de Broglie wavelength corresponding to the dominating frequency.

关键词： schrödinger equation perfectly matched layer

New solitary wave structures to the(3+1)dimensional Kadomtsev-Petviashvili and schrödinger equation

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Journal of Ocean Engineering and Science 2019年第4期4卷 373-378页

作者： Hasan Bulut Emine Nesligül Aksan MiraçKayhan Tukur Abdulkadir Sulaıman Department of Mathematics University of FıratElazıgTurkey Department of Mathematics University of InonuMalatyaTurkey Department of Mathematics Federal University DutseJigawaNigeria

The studies of the dynamic behaviors of nonlinear models arising in ocean engineering play a significant role in our daily *** this paper,an efficient mathematical technique,namely;the sine-Gordon expansion method is employed to construct the traveling wave solutions to the(3+1)-dimensional Kadomtsev-Petviashvili and(3+1)-dimensional nonlinear schrödinger *** suitable values of the parameters,the two-and three-dimensional figures of the obtained solutions are plotted.

关键词： Sine-Gordon expansion method Kadomtsev-Petviashvili equation schrödinger equation wave solutions

High Order Scheme for schrödinger equation with Discontinuous Potential I: Immersed Interface Method

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Numerical Mathematics(Theory,Methods and Applications) 2011年第4期4卷 576-597页

作者： Hao Wu Department of Mathematical Sciences Tsinghua UniversityBeijing10084China

The immersed interface method is modified to compute schrödinger equation with discontinuous *** building the jump conditions of the solution into the finite difference approximation near the interface,this method can give at least second order convergence rate for the numerical solution on uniform cartesian *** accuracy of this algorithm is tested via several numerical examples.

关键词： schrödinger equation discontinuous potential immersed interface method finite difference method

Semi-Eulerian and High Order Gaussian Beam Methods for the schrödinger equation in the Semiclassical Regime

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Communications in Computational Physics 2011年第3期9卷 668-687页

作者： Shi Jin Hao Wu Xu Yang Department of Mathematics University of WisconsinMadisonWI 53706USA Department of Mathematical Sciences Tsinghua UniversityBeijing 10084China Program in Applied and Computational Mathematics Princeton UniversityNJ 08544USA

A novel Eulerian Gaussian beam method was developed in[8]to compute the schrödinger equation efficiently in the semiclassical *** this paper,we introduce an efficient semi-Eulerian implementation of this *** new algorithm inherits the essence of the Eulerian Gaussian beam method where the Hessian is computed through the derivatives of the complexified level set functions instead of solving the dynamic ray tracing *** difference lies in that,we solve the ray tracing equations to determine the centers of the beams and then compute quantities of interests only around these *** yields effectively a local level set implementation,and the beam summation can be carried out on the initial physical space instead of the phase *** a consequence,it reduces the computational cost and also avoids the delicate issue of beam summation around the caustics in the Eulerian Gaussian beam ***,the semi-Eulerian Gaussian beam method can be easily generalized to higher order Gaussian beam methods,which is the topic of the second part of this *** numerical examples are provided to verify the accuracy and efficiency of both the first order and higher order semi-Eulerian methods.

关键词： schrödinger equation semi-Eulerian Gaussian beam method high order methods

Global Solutions of Modified One-Dimensional schrödinger equation

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Communications in Mathematical Research 2021年第3期37卷 349-385页

作者： Ting Zhang School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China

In this paper,we consider the modified one-dimensional schrÖdin-ger equation:(D_(t)-F(D))u=λ|u|^(2)u,where F(ζ)is a second order constant coefficients classical elliptic symbol,and with smooth initial datum of sizeε(<<)*** prove that the solution is global-in-time,combining the vector fields method and a semiclassical analysis method introduced by ***,we get a one term asymptotic expansion for u when t→+∞.

关键词： schrödinger equation semiclassical analysis global solution

Undulatory Theory with Paraconsistent Logic (Part II): schrödinger equation and Probability Representation

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Journal of Quantum Information Science 2016年第3期6卷 181-213页

作者： João Inácio Da Silva Filho Laboratory of Applied Paraconsistent Logic Santa Cecilia University Santos Brazil

Part I of this study proved that the Paraconsistent Annotated Logic using two values (PAL2v), known as the Paraquantum Logic (PQL), can represent the quantum by a model comprising two wave functions obtained from interference phenomena in the 2W (two-wave) region of Young’s experiment (double slit). With this model represented in one spatial dimension, we studied in the Lattice of the PQL, with their values represented in the set of complex numbers, the state vector of unitary module and its correspondence with the two wave functions. Based on these considerations, we applied the PQL model for obtaining Paraquantum logical states ψ related to energy levels, following the principles of the wave theory through schrÖdinger’s equation. We also applied the probability theory and Bonferroni’s inequality for demonstrating that quantum wave functions, represented by evidence degrees, are probabilistic functions studied in the PQL Lattice, confirming that the final Paraquantum Logic Model is well suited to studies involving aspects of the wave-particle theory. This approach of quantum theory using Paraconsistent logic allows the interpretation of various phenomena of Quantum Mechanics, so it is quite promising for creating efficient models in the physical analysis and quantum computing processes.

关键词： Paraconsistent Logic Wave Theory Quantum Mechanics Paraquantum Logic schrödinger equation

An Adaptive Multiresolution Ultra-weak Discontinuous Galerkin Method for Nonlinear schrödinger equations

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Communications on Applied Mathematics and Computation 2022年第1期4卷 60-83页

作者： Zhanjing Tao Juntao Huang Yuan Liu Wei Guo Yingda Cheng School of Mathematics Jilin UniversityJilin 130012China Department of Mathematics Michigan State UniversityEast LansingMI 48824USA Department of Mathematics Statistics and PhysicsWichita State UniversityWichitaKS 67260USA Department of Mathematics and Statistics Texas Tech UniversityLubbockTX 70409USA Department of Mathematics Department of Computational MathematicsScience and EngineeringMichigan State UniversityEast LansingMI 48824USA

This paper develops a high-order adaptive scheme for solving nonlinear schrödinger *** solutions to such equations often exhibit solitary wave and local structures,which make adaptivity essential in improving the simulation *** scheme uses the ultra-weak discontinuous Galerkin(DG)formulation and belongs to the framework of adaptive multiresolution *** numerical experiments are presented to demon-strate the excellent capability of capturing the soliton waves and the blow-up phenomenon.

关键词： Multiresolution Sparse grid Ultra-weak discontinuous Galerkin method schrödinger equation Adaptivity