Exact solutions and wave interactions for one-dimensional two-phase thin film model of a perfectly soluble antisurfactant

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2025-09-22 DOI:10.1016/j.ijnonlinmec.2025.105262

Hari Om Jangid , Subhankar Sil , T. Raja Sekhar

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Abstract

In this article, we obtain some exact solutions to a new hyperbolic system of quasilinear partial differential equations which describes the two-phase thin film model of a perfectly soluble antisurfactant by using symmetry analysis. Lie’s method provides a group of transformations for which the set of solutions remains invariant and through the help of push-forward actions, optimal classes are constructed. The aid of optimal classes facilitates exact solutions of the system. Additionally, we compute some traveling wave solutions of the governing system with the help of special transformations. For each phase, the evolution of the film thickness and concentration gradient is characterized by geometric representation of the solutions. The weak discontinuity behavior across a solution curve is analyzed as time progresses. In addition, the propagation of characteristic shock and the corresponding collision between the characteristic shock and the weak discontinuity are discussed. The reflected and transmitted wave amplitudes, along with the jump in shock acceleration influenced by the incident wave after interaction, are computed.

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.