A NEW APPROACH FOR SOLITON SOLUTIONS OF RLW EQUATION AND (1+2)-DIMENSIONAL NONLINEAR SCHR ¨ ODINGER’S EQUATION ALI FILIZ, ABDULLAH SONMEZOGLU, MEHMET EKICI and DURGUN DURAN Communicated by Horia Cornean In this paper, we introduce a new version of the trial equation method for solv- ing non-integrable partial differential equations in mathematical physics. The exact traveling wave solutions including soliton solutions, singular soliton so- lutions, rational function solutions and elliptic function solutions to the RLW equation and (1+2)-dimensional nonlinear Schr¨odinger’s equation in dual-power law media are obtained by this method. AMS 2010 Subject Classification: 35Q51, 47J35, 74J35. Key words: extended trial equation method, RLW equation, (1+2)-dimensional nonlinear Schr¨odinger’s equation in dual-power law media, soliton solution, elliptic solutions. 1. INTRODUCTION In recent years, there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called solitons and the associated development of a method of solution to two class of nonlinear wave equations termed the reg- ularized long-wave (RLW) equation and the nonlinear Schr¨odinger’s equation (NLSE). The RLW equation arises in the study of shallow-water waves. The generalized version of the RLW equation is known as the R(m,n) equation. The NLSE is an example of a universal nonlinear model that describes many physical nonlinear systems. The equation can be applied to hydrodynam- ics, nonlinear optics, nonlinear acoustics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. A soliton phe- nomenon is an attractive field of present day research in nonlinear physics and mathematics. Essential ingredients in the soliton theory are the RLW equation and the NLSE, and their variants appearing in a wide spectrum of problems. Solitons are identified with a certain class of reflectionless solutions of the inte- grable equations. Such equations, including the RLW equation and the NLSE, MATH. REPORTS 17(67), 1 (2015), 43–56