OICC Press Mathematical Sciences 2251-7456 18 2 (June 2024) 2022 12 16 Exploration of some novel solutions to a coupled Schrödinger–KdV equations in the interactions of capillary-gravity waves 10.1007/s40096-022-00501-0 EN Dipankar Kumar Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, 8100, BD Ahmet Yildirim Department of Mathematics, Faculty of Science, Ege University, Bornova, Izmir, 35100, TR Mohammed K. A. Kaabar Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur, 50603, MY Hadi Rezazadeh Faculty of Modern Technologies Engineering, Amol University of Special Modern Technologies, Amol, IR Mohammad Esmael Samei Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, IR Journal Article 2022 12 16 Abstract Some novel solutions to a system of coupled Schrödinger–Korteweg–de Vries equations are explored in this work by employing the extended sinh-Gordon equation expansion method to the proposed system. Some novel forms of explicit complex hyperbolic and complex trigonometric function solutions such as singular, combined singular, dark, bright, combined dark–bright, periodic wave, dipole soliton, and other solutions are retrieved and explored into their corresponding system via MAPLE software. Two- and three-dimensional graphs are provided to illustrate this study’s novelty. All combined solutions are particularly new in the interactions of capillary-gravity water waves. Extended sinh-Gordon equation expansion method provides an effective tool to explore new precise wave solutions and overcome the difficulties of the ansatz method. All our results in this work play an essential role in explaining various phenomena in ocean and coastal engineering.