In this paper we introduce a forced Kawahara equation. We
solve it making use of a direct ansatz method.
We also solve it via splines method. Numerical examples illlustrate the
accuracy of the obtained results.
Author(s) Details:
Alvaro H. Salas S.,
Fizmako Research Group, Universidad Nacional de Colombia, Colombia.
Please see the link here: https://stm.bookpi.org/RUMCS-V4/article/view/14098
Using a newly developed methodology known as an extended modified auxiliary equation mapping method and three parameters, we were able to find a variety of new families of exact travelling wave solutions, including triangular-type solutions, periodic and doubly periodic like solutions, combined soliton like solutions, kink and anti kink type soliton like solutions, and kink and anti kink type soliton like solutions. In various fields of physics, such as quantum mechanics, hydrodynamics, plasma physics, and quantum field theory for studying the dynamics of Langmuir solitons that appear in nonlinear optics, the Maccari System is a well-known model for dening the dynamics of isolated waves that are localised in a very small part of space. We utilised Mathematica 10.4 to express the physical description of our newly discovered solutions graphically in order to better illustrate the behaviour of different shapes of solutions. The computing work and efficiency of the method illustrate its reliability, straightforwardness, and simplicity for solving various nonlinear complex partial differential equations.
This research focuses on a new approach to the application of physical variables in complex patient therapy. The author believes that it is important to rethink technical characteristics and exposure of the physiotherapeutic factor affecting the organism based on experimental research results, taking into account the nosological form of the disease and the particulars of the individual patient. In this regard, the author introduced new clinical physiotherapy tasks and proposed seven concepts for new physical factor classification in complex patient therapy. The author proposed new ideas in medicine on the basis of research: 1) the human body as a "biological scanning tunnelling microscope"; 2) the human being as part of "nature" refers to the general law of the universe: "singularity and indivisibility of time, matter and shape" as well as the powers of their interaction in continuous constant motion without end. Eventually, the efficacy and protection of physiotherapy relies on the ability of the practitioner to accurately assess all these variables. Both clinical medicine and experimental physiotherapy need to be focused on deep understanding.
Author (s) DetailsAspects of motion theory for the continuous gaseous medium are presented with a substantial influence of dispersion effects related to the microstructure of the medium or to the presence of electromagnetic or gravitational fields of internal force. The precise stationary solutions of non-linear equations are studied in detail in the vicinity of transition fronts and in the form of solitary waves: "classical" and "particle-like" solitons. Various gasdynamic models are seen, beginning with the acoustic relativity theory and the supercritical analog of the special relativity theory up to the Newtonian dark matter and microstructural turbulence model. A number of examples taken from gas dynamics and physics demonstrate typical conformities of the investigated processes.
Author(s) Details