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This research studies the high-energy Klein–Gordon equation, related to the relativistic Schrödinger wave equation. Solutions are produced using the Kudryashov transform and conventional wave transform. The study’s most significant finding is the examination of the physical and mathematical differences in the traveling wave solutions, derived using two alternative transformations. The graphs of the intensity of the wave function and the conclusions at various velocity levels are also examined. The stability analysis of the moving waves, which coincides with Graham’s diffusion law, of the relationship between wave velocity and density is examined and its relationship with the propagation equation is investigated.

We implement the generalized Jacobi elliptic function method with symboliccomputation to construct periodic solutions for the symmetric regularized long wave(SRLW) equation and (1+1)-dimensional dispersive long wave equation.

Geniş bir yüz ölçümüne sahip Sivas'ta idari bölünmenin dışında halkın kendince isimlendirdiği yöreler vardır. Bunlar; Emlek Yöresi, Çamşıhı Yöresi ve İlbeyi/Elbeyi Yöresidir. Bu yörelerin hepsinde de edebiyatımızda iz bırakmış önemli halk şairleri yetişmiştir. Tamamı Türkmen olan Elbeyi yöresinde de otuza yakın halk şairi vardır. Hitabî, İsmetî, Noksanî ve Perişanî bu isimlerin başında gelir, Sivas is a large city. Except for the administrative divisions, there are other regions named by people. These are Emlek, Çamşıhı and İlbeyi / Elbeyi regions. Some prominant folk poets have been grown up in all these regions, who have influenced our oral literature. There are about thirty folk poets in Elbeyi region, all of whom are Turkomen. The prominent of these folk poets are Hitabî, İsmetî, Noksanî and Perişanî

We demonstrate cascade manipulation between magic number gold-fullerene hybrid clusters by channelling thermal energy into a specific reaction pathway with a trigger from the tip of a scanning tunnelling microscope (STM). The (C-60)(m)-Au-n clusters, formed via self-assembly on the Au(111) surface, consist of n Au atoms and m C-60 molecules; the three smallest stable clusters are (C-60)(7)-Au-19, (C-60)(10)-Au-35, and (C-60)(12)-Au-49. The manipulation cascade was initiated by driving the STM tip into the cluster followed by tip retraction. Temporary, partial fragmentation of the cluster was followed by reorganization. Self-selection of the correct numbers of Au atoms and C-60 molecules led to the formation of the next magic number cluster. This cascade manipulation is efficient and facile with an extremely high selectivity. It offers a way to perform on-surface tailoring of atomic and molecular clusters by harnessing thermal energy, which is known as the principal enemy of the quest to achieve ultimate structural control with the STM.