Galiev Sh. U., Galiyev T. Sh.
Department of Mechanical Engineering, The University of Auckland, Private Bag 92019, Auckland 1, New Zealand.
Chaos. 2001 Sep;11(3):686-704. doi: 10.1063/1.1394190.
Perturbed wave equations are considered. Approximate general solutions of these equations are constructed, which describe wave phenomena in different physical and chemical systems. Analogies between surface waves, nonlinear and atom optics, field theories and acoustics of the early Universe can be seen in the similarities between the general solutions that govern each system. With the help of the general solutions and boundary conditions and/or resonant conditions we have derived the basic highly nonlinear ordinary differential equation or the basic algebraic equation for traveling waves. Then, approximate analytic resonant solutions are constructed, which describe the trans-resonant transformation of harmonic waves into traveling shock-, jet-, or mushroom-like waves. The mushroom-like waves can evolve into cloud-like and vortex-like structures. The motion and oscillations of these waves and structures can be very complex. Under parametric excitation these waves can vary their velocity, stop, and change the direction of their motion. Different dynamic patterns are yielded by these resonant traveling waves in the x-t and x-y planes. They simulate many patterns observed in liquid layers, optical systems, superconductors, Bose-Einstein condensates, micro- and electron resonators. The harmonic excitation may be compressed and transformed inside the resonant band into traveling or standing particle-like waves. The area of application of these solutions and results may possibly vary from the generation of nuclear particles, acoustical turbulence, and catastrophic seismic waves to the formation of galaxies and the Universe. In particular, the formation of galaxies and galaxy clusters may be connected with nonlinear and resonant phenomena in the early Universe. (c) 2001 American Institute of Physics.
考虑了微扰波动方程。构建了这些方程的近似通解，其描述了不同物理和化学系统中的波动现象。表面波、非线性与原子光学、场论以及早期宇宙声学之间的类比可以从支配每个系统的通解之间的相似性中看出。借助通解以及边界条件和/或共振条件，我们推导出了行波的基本高度非线性常微分方程或基本代数方程。然后，构建了近似解析共振解，其描述了谐波向行波状激波、射流或蘑菇状波的跨共振转变。蘑菇状波可以演变成云状和涡状结构。这些波和结构的运动与振荡可能非常复杂。在参数激励下，这些波可以改变其速度、停止并改变运动方向。这些共振行波在x - t和x - y平面中产生不同的动态模式。它们模拟了在液层、光学系统、超导体、玻色 - 爱因斯坦凝聚体、微谐振器和电子谐振器中观察到的许多模式。谐波激励在共振带内可能被压缩并转变为行波状或驻波状粒子波。这些解和结果的应用领域可能从核粒子的产生、声学湍流和灾难性地震波到星系和宇宙的形成不等。特别是，星系和星系团的形成可能与早期宇宙中的非线性和共振现象有关。(c) 2001美国物理研究所。
