A Wick-type stochastic space and with GDCOs may be given as
A Wick-type stochastic space and with GDCOs is usually given as the form: i l,1 U + 1 ( p ) pl 2l,2 U + |U | q2lU + i two ( p )3l,three U = 0, ( p, q) R+ R, q3l(14)The two functions 1 and 2 are nonzero, integrable, and defined from R+ inside a variety that’s contained in (k)-1 . The stochastic CFT8634 Purity & Documentation equation (14) would be the perturbed form with the next Schr inger irota equation with GDCOs: i l,1 u 2l,2 u 3l,2 u + 1 ( p ) + | u |2 u + i two ( p ) = 0, pl q2l q3l (15)where 1 , 2 are deterministic, nonzero, and integrable functions defined on R+ . To resolve the stochastic Schr inger irota Equation (14), we only seek its exact options inside a white noise space. From Equation (14), the Hermite transform, and Relation (six), we receive the deterministic conformable equation: i l,1 U ( p, q, z) 2l,2 U ( p, q, z) + 1 ( p, z) + |U ( p, q, z)|2 U ( p, q, z) pl q2l+ i two ( p, z)3l,two U ( p, q, z) = 0, q3l(16)exactly where z = (z1 , z2 , . . .) (CN )c . 4.1. Deterministic Traveling Wave Options To extract the solutions of Equation (16) in traveling wave kind, we impose the identities 1 ( p, z) = 1 ( p, z), 2 ( p, z) = 2 ( p, z), U ( p, q, z) = u( p, q, z), plus the transformation: u( p, q, z) = u(w( p, q, z)) = Z (w) exp i c w( p, q, z) = -2dp 0 pT ()d +d 1 (, l )qd two (, l ), (17)T ()d + 1 (, l )qd , two (, l )where c, d R and T is really a function to be specified. From Theorem 1 and also the transformation (17), we’ve: l,1 u = T ( p) -2dZ (w) + icZ (w) exp i c plpT ()d +d 1 (, l )pqd 2 (, l )q,(18)2l,two u = Z (w) + 2idZ (w) – d2 Z (w) exp i c q2lT ()d +d 1 (, l )d 2 (, l ),(19)Mathematics 2021, 9,7 of3l,two u q3l=Z (w) + 3i dZ (w) – 3d2 Z (w) – id3 Z (w)pexp i cT ()d +d 1 (, l )qd 2 (, l ).(20)By substituting Equations (18)20) into Equation (16) and extracting the imaginary and true parts, we have the differential method:(-2dT ( p) + 21 ( p, z) – 3d2 ( p, z)) Z (w) + 2 ( p, z) Z (w) = 0, -cT ( p) – d2 1 ( p, z) + d3 two ( p, z) Z (w) + (1 ( p, z) – 3d2 ( p, z)) Z (w) + Z3 (w) = 0.(21)Based on the generalized Kudryashov scheme plus the homogeneous balance for z (w) and z3 (w), we can acquire = 4, = 1, as well as the wave remedy of Equation (16) may be imposed as the kind:u(w( p, q, z)) =j =Bj ( p, z)E (w( p, q, w))ji =0Ai ( p, z)Ei (w( p, q, z)), (22)where Ai , Bj (i = 0, . . . , 4, j = 0, 1) are functions to be specified and E Cholesteryl sulfate site represents a option of Equation (12). Inserting Equations (22) and (12) for = 3 into (21) offers a polynomial equation in the powers of E. Placing the coefficients that involve the comparable exponents of E as zero, we extract an algebraic nonlinear method of equations in Ai , Bj (i = 0, . . . , 4, j = 0, 1) and T ( p). Handling this system by means of the Mathematica plan gives the next groups of values. Group 1: three 2 80B0 two 2 eight two B0 (1 – 3d2 ) A0 = A0 , A1 = A2 = 0, A3 = – , A4 = – A0 A0 six 4 2 2 two two B0 = B0 , B1 = 0, T = A0 – d B0 1 + d A0 B0 2 , 2 cB(23)where A0 and B0 are choosable integrable functions on R+ . By employing the values (23), Equations (22) and (13), we deduce a traveling wave resolution to Equation (16) as the type: u1 ( p, q, z) = A0 ( p, z) eight 2 l 3 ( p, q, z) B0 ( p, z)[10B0 ( p, z)two ( p, z) + l ( p, q, z)(1 ( p, z) – 3d2 ( p, z))] – , B0 ( p, z) A0 ( p, z) where: l ( p, q, z) = and: w( p, q, z) , B exp(2w( p, q, z)) + (25) (24)= – +2d cqp2 four ( A2 (, z) – d2 B0 (, z)1 (, z) + d6 A0 (, z) B0 (, z)two (, z))d 0 two two B0 ( p, z)1 (t, l )d , 2 (, l )(26)provided that 0 and A0 B0 = 0.Mathematics 2021, 9,8 ofGroup two: 3 2 A0 = A0 , A = 32B0 two , A2.
