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(21 citation statements)

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“…Using the Bell polynomials, we have obtained Hirota Bilinear Form (16) of (2). By virtue of (16), two kinds of the multi-soliton solutions [i.e., (31) and (17)] and another kind of the analytic solutions [i.e., (37)] have been obtained, both with different nonlinear dispersion relations, as illustrated in Figures 1-7. For investigating the integrability of (2), we have obtained Lax Pairs (38) and BTs (44) for (2), with our integrability results as the multi-soliton solutions.…”

confidence: 99%

“…Using the Bell polynomials, we have obtained Hirota Bilinear Form (16) of (2). By virtue of (16), two kinds of the multi-soliton solutions [i.e., (31) and (17)] and another kind of the analytic solutions [i.e., (37)] have been obtained, both with different nonlinear dispersion relations, as illustrated in Figures 1-7. For investigating the integrability of (2), we have obtained Lax Pairs (38) and BTs (44) for (2), with our integrability results as the multi-soliton solutions.…”

confidence: 99%

“…Higher-dimensional NLEEs are scientifically interesting: For example, some (3+1)-dimensional KdV-type equations can describe the dust-ion-acoustic waves in cosmic nonmagnetised dusty plasmas such as those in the supernova shells and Saturn's F-ring [28], and some (3+1)-dimensional NLEEs, with certain parameters, can reduce to the (2+1)-dimensional and (1+1)-dimensional NLEEs [29][30][31][32][33][34][35] where u is an analytic function depending on the scaled spatial coordinates (x, y, z) and temporal coordinate t. By virtue of the exp-function method [10] and bilinear method via the logarithm transformation [36], the soliton solutions of (2) have been discussed [10,36]. In the fluid and plasma dynamics, special cases of (2) are seen as follows: (a) When y = z, u(x, y, t) = (η, t) = [x + χ(y), t] with as χ an analytic function of y, (2) degenerates into the KdV equation [37],…”

confidence: 99%

“…We make the transformation By using the general mapping deformation method [10,40], we can obtain the following solutions of the corresponding undisturbed Eq. (70) when f ¼ 0.…”

confidence: 99%