多年來，劉希強(qiáng)教授一直從事應(yīng)用數(shù)學(xué)方面的研究工作. 目前主要從事非線性偏微分方程解的應(yīng)用研究. 正主持國家自然科學(xué)基金和中國工程物理研究院基金聯(lián)合資助項(xiàng)目”流體力學(xué)方程和粒子輸運(yùn)方程人為解的應(yīng)用研究”課題, 該課題屬于數(shù)學(xué)、物理在國防核工業(yè)中的應(yīng)用研究,也是國際上程序驗(yàn)證和確認(rèn)(V and V)中重點(diǎn)關(guān)注的問題之一。在非線性微分系統(tǒng)的精確解研究方面，已主持完成山東省自然科學(xué)基金資助項(xiàng)目2項(xiàng),參與山東省自然科學(xué)基金資助項(xiàng)目2項(xiàng). 近幾年來國內(nèi)外專業(yè)期刊發(fā)表論文40余篇, 其中SCI和EI論文30余篇. 獲山東省高校優(yōu)秀科研成果一等獎(jiǎng)一項(xiàng), 獲山東省自然科學(xué)獎(jiǎng)三等獎(jiǎng)一項(xiàng). 在已培養(yǎng)畢業(yè)的12名研究生中,考取攻讀博士學(xué)位2名, 4人次獲山東省研究生優(yōu)秀科技創(chuàng)新成果獎(jiǎng)三等獎(jiǎng)2項(xiàng), 一人獲山東省優(yōu)秀畢業(yè)研究生稱號(hào), 多人獲聊城大學(xué)優(yōu)秀畢業(yè)論文和燎原獎(jiǎng)學(xué)金。

先后主持國家自然科學(xué)基金項(xiàng)目1項(xiàng)、主持或承擔(dān)山東省自然科學(xué)基金項(xiàng)目4項(xiàng)、山東省軟科學(xué)項(xiàng)目1項(xiàng)。
一、主要科研項(xiàng)目
1. 流體力學(xué)方程與粒子輸運(yùn)方程人為解的應(yīng)用研究, 2011-2013,國家自然科學(xué)基金與中物院聯(lián)合基金 (11076015).
2. 四元數(shù)對(duì)稱群方法在波方程求解中 的應(yīng)用. 2008-2010, 山東省自然科學(xué)基金(Y2008A35).
3. 高維非線性方程不變解的研究。2004-2006.山東省自然科學(xué)基金(2004zx16).
4．非連續(xù)孤子系統(tǒng)的局域激發(fā)及其性質(zhì)研究. 2007-2009, 山東省自然科學(xué)基金(2007G64).
5. 高維非線性系統(tǒng)的局域激發(fā)模式及相互作用行為的研究.2005-2007, 山東省自然科學(xué)基金(Q2005A01).
二、主要科研獲獎(jiǎng)
1. 灰色經(jīng)濟(jì)預(yù)測(cè)模型及其應(yīng)用, 獲山東省科學(xué)技術(shù)協(xié)會(huì)專著三等獎(jiǎng),1998.
2. 均衡問題及其在微分方程中的應(yīng)用.山東省高等學(xué)校優(yōu)秀科研成果獎(jiǎng)一等獎(jiǎng).山東省教育廳.2009.
3. 幾類非線性發(fā)展方程的 精確解及守恒律.,山東省研究生優(yōu)秀科技創(chuàng)新成果三等獎(jiǎng).,2009.
4. 非線性發(fā)展方程的精確解, 山東省研究生優(yōu)秀科技創(chuàng)新成果三等獎(jiǎng).,2010.
5. 廣義凸性和廣義單調(diào)性及其在微分方程和 控制 系統(tǒng)中的應(yīng)用, 山東科學(xué)技術(shù)獎(jiǎng)三等獎(jiǎng),2011.
三、主要專著
1. 灰色關(guān)聯(lián)空間引論。貴州人民出版社,1993年.
2. 灰色經(jīng)濟(jì)預(yù)測(cè)模型及其應(yīng)用, 黃河出版社,1996年.
四、主要論文
1. Some exact solutions of the variable coefficient Schrodinger equation, Commun. in Nonlinear Sci. and Num. Simul., 12 (2007).1355-1359.
2. A Direct Transformation Method and its Application to Variable Coefficient Nonlinear Equations of Schrodinger Type, Z. Naturforsch. 64a, (2009) ,697-708.
3. New exact solutions and conservation laws of the (2 +1)-dimensional dispersive long wave equations, Phys. Lett. A 373 (2009) 214-220.
4. The direct symmetry method and its application in variable coefficients Schrodinger equation, Appl. Math. Comput. 187 (2007) 701-707.
5. Symmetry, Reductions and New Exact Solutions of ANNV Equation Through Lax Pair, Commun. Theor. Phys. 50 (2008) . 1u20136.
6. Similarity Reductions and Similarity Solutions of the (3+1)-Dimensional Kadomtsev-Petviashvili Equation, Chin. Phys. Lett., 25, 10 (2008) 3527.
7. Classification, reduction, group invariant solutions and conservation laws of the Gardner-KP equation, Appl. Math. Comput. 215 (2009) 1244.
8. Exact Solutions to (2+1)-Dimensional Kaup Kupershmidt Equation, Commun. Theor. Phys. 52 (2009) pp. 795-800.
9. Exact solutions and conservation laws of (2 + 1)-dimensional Boiti-Leon-Pempinelli equation, Appl. Math. Comput. 216 (2010) 2293-2300.
10. A generalized Gu2019/G-expansion method and its applications to nonlinear evolution equations, Appl. Math. Comput. 215 (2010) 3811-3816.
11. Explicit solutions of the (2 + 1)-dimensional AKNS shallow water wave equation with variable coefficients, Appl. Math. Comput. 217 (2010) 1287.
12. Explicit solutions of the Bogoyavlensky-Konoplechenko equation, Appl. Math. Comput. 215 (2010) 3669-3673.
13. Symmetry reduction, exact solutions and conservation laws of the Sawada-Kotera-Kadomtsev-Petviashvili equation, Appl. Math. Comput. 216 (2010) 1065-1071.
14. Explicit solutions of the generalized KdV equations with higher order nonlinearity, Appl. Math. Comput. 171 (2005) 315-319.
15. Symmetry Reductions, Exact Solutions and Conservation Laws of Asymmetric Nizhnik Novikov Veselov Equation, Commun. Theor. Phys. 49 (2008) pp. 1u20138.
16. Explicit Solutions of (2+1)-Dimensional Canonical Generalized KP, KdV, and (2+1)-Dimensional Burgers Equations with Variable Coefficients, Commun. Theor. Phys. 52 (2009) pp. 784u2013790.
17. Symmetry Groups and New Exact Solutions to(2-+-1)-Dimensional Variable Coefficient Canonical Generalized KP Equation, Commun．Theor．Phys．48(2007)PP．405-410.
18. Study of(2+1)-Dimensional Higher-Order Broer-Kaup System, Commun．Theor．Phys 7(2007)PP．403-408.
19. Symmetry reductions and exact solutions of the (2 + 1)-dimensional Jaulent-Miodek equation, Appl. Math. Comput. 219 (2012) 911-916.
20. Symmetries and Exact Solutions of the Breaking Soliton Equation, Commun. Theor. Phys. 56 (2011) 851u2013855.
21. New Multiple Soliton-like and Periodic Solutions for (2+1)-Dimensional Canonical Generalized KP Equation with Variable Coefficients, Commun. Theor. Phys. 46 (2006) pp. 793u2013798.